TSTP Solution File: GRP624+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP624+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 22:28:54 EDT 2022
% Result : Theorem 2.87s 2.01s
% Output : Proof 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP624+1 : TPTP v8.1.0. Released v3.4.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n024.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Aug 31 18:17:34 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 2.87/2.01 % SZS status Theorem
% 2.87/2.01 % SZS output start Proof
% 2.87/2.01 tff(k1_binop_1_type, type, (
% 2.87/2.01 k1_binop_1: ( $i * $i * $i ) > $i)).
% 2.87/2.01 tff(tptp_fun_C_2_type, type, (
% 2.87/2.01 tptp_fun_C_2: $i)).
% 2.87/2.01 tff(tptp_fun_B_1_type, type, (
% 2.87/2.01 tptp_fun_B_1: $i)).
% 2.87/2.01 tff(u1_group_1_type, type, (
% 2.87/2.01 u1_group_1: $i > $i)).
% 2.87/2.01 tff(g1_group_1_type, type, (
% 2.87/2.01 g1_group_1: ( $i * $i ) > $i)).
% 2.87/2.01 tff(k2_autgroup_type, type, (
% 2.87/2.01 k2_autgroup: $i > $i)).
% 2.87/2.01 tff(tptp_fun_A_0_type, type, (
% 2.87/2.01 tptp_fun_A_0: $i)).
% 2.87/2.01 tff(k1_autgroup_type, type, (
% 2.87/2.01 k1_autgroup: $i > $i)).
% 2.87/2.01 tff(k2_binop_1_type, type, (
% 2.87/2.01 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 2.87/2.01 tff(u1_struct_0_type, type, (
% 2.87/2.01 u1_struct_0: $i > $i)).
% 2.87/2.01 tff(k7_funct_2_type, type, (
% 2.87/2.01 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 2.87/2.01 tff(l1_group_1_type, type, (
% 2.87/2.01 l1_group_1: $i > $o)).
% 2.87/2.01 tff(v1_group_1_type, type, (
% 2.87/2.01 v1_group_1: $i > $o)).
% 2.87/2.01 tff(m1_relset_1_type, type, (
% 2.87/2.01 m1_relset_1: ( $i * $i * $i ) > $o)).
% 2.87/2.01 tff(k2_zfmisc_1_type, type, (
% 2.87/2.01 k2_zfmisc_1: ( $i * $i ) > $i)).
% 2.87/2.01 tff(m2_relset_1_type, type, (
% 2.87/2.01 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.87/2.01 tff(v1_funct_2_type, type, (
% 2.87/2.01 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.87/2.01 tff(v1_funct_1_type, type, (
% 2.87/2.01 v1_funct_1: $i > $o)).
% 2.87/2.01 tff(v4_group_1_type, type, (
% 2.87/2.01 v4_group_1: $i > $o)).
% 2.87/2.01 tff(v3_group_1_type, type, (
% 2.87/2.01 v3_group_1: $i > $o)).
% 2.87/2.01 tff(v3_struct_0_type, type, (
% 2.87/2.01 v3_struct_0: $i > $o)).
% 2.87/2.01 tff(m2_fraenkel_type, type, (
% 2.87/2.01 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 2.87/2.01 tff(k4_autgroup_type, type, (
% 2.87/2.01 k4_autgroup: $i > $i)).
% 2.87/2.01 tff(tptp_fun_C_3_type, type, (
% 2.87/2.01 tptp_fun_C_3: ( $i * $i ) > $i)).
% 2.87/2.01 tff(tptp_fun_D_4_type, type, (
% 2.87/2.01 tptp_fun_D_4: ( $i * $i ) > $i)).
% 2.87/2.01 tff(m1_subset_1_type, type, (
% 2.87/2.01 m1_subset_1: ( $i * $i ) > $o)).
% 2.87/2.01 tff(m1_fraenkel_type, type, (
% 2.87/2.01 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 2.87/2.01 tff(v1_xboole_0_type, type, (
% 2.87/2.01 v1_xboole_0: $i > $o)).
% 2.87/2.01 tff(l1_struct_0_type, type, (
% 2.87/2.01 l1_struct_0: $i > $o)).
% 2.87/2.01 tff(v1_fraenkel_type, type, (
% 2.87/2.01 v1_fraenkel: $i > $o)).
% 2.87/2.01 tff(1,plain,
% 2.87/2.01 ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k1_binop_1(k2_autgroup(A!0), B!1, C!2)) <=> (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 2.87/2.01 inference(commutativity,[status(thm)],[])).
% 2.87/2.01 tff(2,plain,
% 2.87/2.01 (^[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)))),
% 2.87/2.01 inference(bind,[status(th)],[])).
% 2.87/2.01 tff(3,plain,
% 2.87/2.01 (![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))),
% 2.87/2.01 inference(quant_intro,[status(thm)],[2])).
% 2.87/2.01 tff(4,plain,
% 2.87/2.01 (![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))),
% 2.87/2.01 inference(rewrite,[status(thm)],[])).
% 2.87/2.01 tff(5,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 2.87/2.01 tff(6,plain,
% 2.87/2.01 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.87/2.01 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.87/2.01 tff(7,plain,(
% 2.87/2.01 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.87/2.01 inference(skolemize,[status(sab)],[6])).
% 2.87/2.01 tff(8,plain,
% 2.87/2.01 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.87/2.01 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.87/2.01 tff(9,plain,
% 2.87/2.01 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))),
% 2.87/2.01 inference(quant_inst,[status(thm)],[])).
% 2.87/2.01 tff(10,plain,
% 2.87/2.01 (m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.01 inference(unit_resolution,[status(thm)],[9, 8])).
% 2.87/2.01 tff(11,plain,
% 2.87/2.01 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))))),
% 2.87/2.01 inference(bind,[status(th)],[])).
% 2.87/2.01 tff(12,plain,
% 2.87/2.01 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 2.87/2.01 inference(quant_intro,[status(thm)],[11])).
% 2.87/2.01 tff(13,plain,
% 2.87/2.01 (^[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) | (~v1_group_1(A)) | (~l1_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)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_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)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), rewrite((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))))),
% 2.87/2.01 inference(bind,[status(th)],[])).
% 2.87/2.01 tff(14,plain,
% 2.87/2.01 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 2.87/2.01 inference(quant_intro,[status(thm)],[13])).
% 2.87/2.01 tff(15,plain,
% 2.87/2.01 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(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))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 2.87/2.01 inference(rewrite,[status(thm)],[])).
% 2.87/2.01 tff(16,plain,
% 2.87/2.01 (^[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)))), rewrite(((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 2.87/2.01 inference(bind,[status(th)],[])).
% 2.87/2.01 tff(17,plain,
% 2.87/2.01 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(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))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 2.87/2.01 inference(quant_intro,[status(thm)],[16])).
% 2.87/2.01 tff(18,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_autgroup')).
% 2.87/2.01 tff(19,plain,
% 2.87/2.01 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 2.87/2.01 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.87/2.01 tff(20,plain,
% 2.87/2.01 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 2.87/2.01 inference(modus_ponens,[status(thm)],[19, 15])).
% 2.87/2.01 tff(21,plain,(
% 2.87/2.01 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 2.87/2.01 inference(skolemize,[status(sab)],[20])).
% 2.87/2.01 tff(22,plain,
% 2.87/2.01 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 2.87/2.01 inference(modus_ponens,[status(thm)],[21, 14])).
% 2.87/2.01 tff(23,plain,
% 2.87/2.01 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[22, 12])).
% 2.87/2.02 tff(24,plain,
% 2.87/2.02 ((((~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), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))) <=> ((~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), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(25,plain,
% 2.87/2.02 (((~(~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))))) <=> (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(26,plain,
% 2.87/2.02 ((~(~((~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))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(27,plain,
% 2.87/2.02 (((~(~((~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), k4_autgroup(A!0)))) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))) <=> (((~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), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))))))),
% 2.87/2.02 inference(monotonicity,[status(thm)],[26, 25])).
% 2.87/2.02 tff(28,plain,
% 2.87/2.02 (((~(~((~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), k4_autgroup(A!0)))) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))) <=> ((~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), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))),
% 2.87/2.02 inference(transitivity,[status(thm)],[27, 24])).
% 2.87/2.02 tff(29,plain,
% 2.87/2.02 ((~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))) <=> (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B))))))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(30,plain,
% 2.87/2.02 ((~![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), k4_autgroup(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))) <=> (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B))))))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(31,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), k4_autgroup(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t15_autgroup')).
% 2.87/2.02 tff(32,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[31, 30])).
% 2.87/2.02 tff(33,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[32, 29])).
% 2.87/2.02 tff(34,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[33, 29])).
% 2.87/2.02 tff(35,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[34, 29])).
% 2.87/2.02 tff(36,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[35, 29])).
% 2.87/2.02 tff(37,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[36, 29])).
% 2.87/2.02 tff(38,plain,
% 2.87/2.02 (~![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), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[37, 29])).
% 2.87/2.02 tff(39,plain,
% 2.87/2.02 ((~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), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[38, 28])).
% 2.87/2.02 tff(40,plain,
% 2.87/2.02 (l1_group_1(A!0)),
% 2.87/2.02 inference(and_elim,[status(thm)],[39])).
% 2.87/2.02 tff(41,plain,
% 2.87/2.02 (v4_group_1(A!0)),
% 2.87/2.02 inference(and_elim,[status(thm)],[39])).
% 2.87/2.02 tff(42,plain,
% 2.87/2.02 (v3_group_1(A!0)),
% 2.87/2.02 inference(and_elim,[status(thm)],[39])).
% 2.87/2.02 tff(43,plain,
% 2.87/2.02 (v1_group_1(A!0)),
% 2.87/2.02 inference(and_elim,[status(thm)],[39])).
% 2.87/2.02 tff(44,plain,
% 2.87/2.02 (~v3_struct_0(A!0)),
% 2.87/2.02 inference(and_elim,[status(thm)],[39])).
% 2.87/2.02 tff(45,plain,
% 2.87/2.02 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(46,plain,
% 2.87/2.02 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 2.87/2.02 inference(quant_inst,[status(thm)],[])).
% 2.87/2.02 tff(47,plain,
% 2.87/2.02 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 2.87/2.02 inference(modus_ponens,[status(thm)],[46, 45])).
% 2.87/2.02 tff(48,plain,
% 2.87/2.02 (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 2.87/2.02 inference(unit_resolution,[status(thm)],[47, 44, 43, 42, 41, 40, 23])).
% 2.87/2.02 tff(49,plain,
% 2.87/2.02 (((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(tautology,[status(thm)],[])).
% 2.87/2.02 tff(50,plain,
% 2.87/2.02 (m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(unit_resolution,[status(thm)],[49, 48])).
% 2.87/2.02 tff(51,plain,
% 2.87/2.02 ((~(m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(tautology,[status(thm)],[])).
% 2.87/2.02 tff(52,plain,
% 2.87/2.02 ((~(m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(unit_resolution,[status(thm)],[51, 50])).
% 2.87/2.02 tff(53,plain,
% 2.87/2.02 (m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(unit_resolution,[status(thm)],[52, 10])).
% 2.87/2.02 tff(54,plain,
% 2.87/2.02 (((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(tautology,[status(thm)],[])).
% 2.87/2.02 tff(55,plain,
% 2.87/2.02 (v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 2.87/2.02 inference(unit_resolution,[status(thm)],[54, 48])).
% 2.87/2.02 tff(56,plain,
% 2.87/2.02 (((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | v1_funct_1(k2_autgroup(A!0))),
% 2.87/2.02 inference(tautology,[status(thm)],[])).
% 2.87/2.02 tff(57,plain,
% 2.87/2.02 (v1_funct_1(k2_autgroup(A!0))),
% 2.87/2.02 inference(unit_resolution,[status(thm)],[56, 48])).
% 2.87/2.02 tff(58,plain,
% 2.87/2.02 (^[A: $i, B: $i] : refl(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))))),
% 2.87/2.02 inference(bind,[status(th)],[])).
% 2.87/2.02 tff(59,plain,
% 2.87/2.02 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 2.87/2.02 inference(quant_intro,[status(thm)],[58])).
% 2.87/2.02 tff(60,plain,
% 2.87/2.02 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), rewrite((v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))) <=> (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))))),
% 2.87/2.02 inference(bind,[status(th)],[])).
% 2.87/2.02 tff(61,plain,
% 2.87/2.02 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 2.87/2.02 inference(quant_intro,[status(thm)],[60])).
% 2.87/2.02 tff(62,plain,
% 2.87/2.02 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 2.87/2.02 inference(rewrite,[status(thm)],[])).
% 2.87/2.02 tff(63,plain,
% 2.87/2.02 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(64,plain,
% 2.87/2.03 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[63])).
% 2.87/2.03 tff(65,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g1_group_1')).
% 2.87/2.03 tff(66,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.87/2.03 tff(67,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.87/2.03 tff(68,plain,(
% 2.87/2.03 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 2.87/2.03 inference(skolemize,[status(sab)],[67])).
% 2.87/2.03 tff(69,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.87/2.03 tff(70,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[69, 59])).
% 2.87/2.03 tff(71,plain,
% 2.87/2.03 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 2.87/2.03 inference(rewrite,[status(thm)],[])).
% 2.87/2.03 tff(72,plain,
% 2.87/2.03 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 2.87/2.03 inference(quant_inst,[status(thm)],[])).
% 2.87/2.03 tff(73,plain,
% 2.87/2.03 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[72, 71])).
% 2.87/2.03 tff(74,plain,
% 2.87/2.03 ((~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 2.87/2.03 inference(unit_resolution,[status(thm)],[73, 70, 57, 55])).
% 2.87/2.03 tff(75,plain,
% 2.87/2.03 (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 2.87/2.03 inference(unit_resolution,[status(thm)],[74, 53])).
% 2.87/2.03 tff(76,plain,
% 2.87/2.03 (((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 2.87/2.03 inference(tautology,[status(thm)],[])).
% 2.87/2.03 tff(77,plain,
% 2.87/2.03 (l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 2.87/2.03 inference(unit_resolution,[status(thm)],[76, 75])).
% 2.87/2.03 tff(78,plain,
% 2.87/2.03 (((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 2.87/2.03 inference(tautology,[status(thm)],[])).
% 2.87/2.03 tff(79,plain,
% 2.87/2.03 (v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 2.87/2.03 inference(unit_resolution,[status(thm)],[78, 75])).
% 2.87/2.03 tff(80,plain,
% 2.87/2.03 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(81,plain,
% 2.87/2.03 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[80])).
% 2.87/2.03 tff(82,plain,
% 2.87/2.03 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(rewrite,[status(thm)],[])).
% 2.87/2.03 tff(83,plain,
% 2.87/2.03 (^[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))) | (~v1_group_1(A)) | (~l1_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))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(84,plain,
% 2.87/2.03 (![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))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[83])).
% 2.87/2.03 tff(85,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/sandbox2/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 2.87/2.03 tff(86,plain,
% 2.87/2.03 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[85, 84])).
% 2.87/2.03 tff(87,plain,
% 2.87/2.03 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[86, 82])).
% 2.87/2.03 tff(88,plain,(
% 2.87/2.03 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(skolemize,[status(sab)],[87])).
% 2.87/2.03 tff(89,plain,
% 2.87/2.03 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[88, 81])).
% 2.87/2.03 tff(90,plain,
% 2.87/2.03 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 2.87/2.03 inference(rewrite,[status(thm)],[])).
% 2.87/2.03 tff(91,plain,
% 2.87/2.03 (((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) <=> ((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 2.87/2.03 inference(rewrite,[status(thm)],[])).
% 2.87/2.03 tff(92,plain,
% 2.87/2.03 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 2.87/2.03 inference(monotonicity,[status(thm)],[91])).
% 2.87/2.03 tff(93,plain,
% 2.87/2.03 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 2.87/2.03 inference(transitivity,[status(thm)],[92, 90])).
% 2.87/2.03 tff(94,plain,
% 2.87/2.03 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 2.87/2.03 inference(quant_inst,[status(thm)],[])).
% 2.87/2.03 tff(95,plain,
% 2.87/2.03 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.87/2.03 tff(96,plain,
% 2.87/2.03 (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 2.87/2.03 inference(unit_resolution,[status(thm)],[95, 89, 79, 77])).
% 2.87/2.03 tff(97,plain,
% 2.87/2.03 (^[A: $i, B: $i] : refl(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(98,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[97])).
% 2.87/2.03 tff(99,plain,
% 2.87/2.03 (^[A: $i, B: $i] : rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(100,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[99])).
% 2.87/2.03 tff(101,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 2.87/2.03 inference(transitivity,[status(thm)],[100, 98])).
% 2.87/2.03 tff(102,plain,
% 2.87/2.03 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))) <=> ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(103,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[102])).
% 2.87/2.03 tff(104,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 2.87/2.03 inference(rewrite,[status(thm)],[])).
% 2.87/2.03 tff(105,plain,
% 2.87/2.03 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))) <=> ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))))),
% 2.87/2.03 inference(bind,[status(th)],[])).
% 2.87/2.03 tff(106,plain,
% 2.87/2.03 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 2.87/2.03 inference(quant_intro,[status(thm)],[105])).
% 2.87/2.03 tff(107,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g1_group_1')).
% 2.87/2.03 tff(108,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[107, 106])).
% 2.87/2.03 tff(109,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[108, 104])).
% 2.87/2.03 tff(110,plain,(
% 2.87/2.03 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 2.87/2.03 inference(skolemize,[status(sab)],[109])).
% 2.87/2.03 tff(111,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[110, 103])).
% 2.87/2.03 tff(112,plain,
% 2.87/2.03 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 2.87/2.03 inference(modus_ponens,[status(thm)],[111, 101])).
% 2.87/2.03 tff(113,plain,
% 2.87/2.03 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D))))))),
% 2.87/2.04 inference(rewrite,[status(thm)],[])).
% 2.87/2.04 tff(114,plain,
% 2.87/2.04 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D))))))),
% 2.87/2.04 inference(quant_inst,[status(thm)],[])).
% 2.87/2.04 tff(115,plain,
% 2.87/2.04 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[114, 113])).
% 2.87/2.04 tff(116,plain,
% 2.87/2.04 ((~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))),
% 2.87/2.04 inference(unit_resolution,[status(thm)],[115, 112, 57, 55])).
% 2.87/2.04 tff(117,plain,
% 2.87/2.04 (![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))),
% 2.87/2.04 inference(unit_resolution,[status(thm)],[116, 53])).
% 2.87/2.04 tff(118,plain,
% 2.87/2.04 (((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))) <=> ((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | (~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 2.87/2.04 inference(rewrite,[status(thm)],[])).
% 2.87/2.04 tff(119,plain,
% 2.87/2.04 ((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 2.87/2.04 inference(quant_inst,[status(thm)],[])).
% 2.87/2.04 tff(120,plain,
% 2.87/2.04 ((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | (~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[119, 118])).
% 2.87/2.04 tff(121,plain,
% 2.87/2.04 (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 2.87/2.04 inference(unit_resolution,[status(thm)],[120, 117, 96])).
% 2.87/2.04 tff(122,plain,
% 2.87/2.04 (((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 2.87/2.04 inference(tautology,[status(thm)],[])).
% 2.87/2.04 tff(123,plain,
% 2.87/2.04 (k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 2.87/2.04 inference(unit_resolution,[status(thm)],[122, 121])).
% 2.87/2.04 tff(124,plain,
% 2.87/2.04 (u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) = k2_autgroup(A!0)),
% 2.87/2.04 inference(symmetry,[status(thm)],[123])).
% 2.87/2.04 tff(125,plain,
% 2.87/2.04 (k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(k2_autgroup(A!0), B!1, C!2)),
% 2.87/2.04 inference(monotonicity,[status(thm)],[124])).
% 2.87/2.04 tff(126,plain,
% 2.87/2.04 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 2.87/2.04 inference(bind,[status(th)],[])).
% 2.87/2.04 tff(127,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(quant_intro,[status(thm)],[126])).
% 2.87/2.04 tff(128,plain,
% 2.87/2.04 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 2.87/2.04 inference(bind,[status(th)],[])).
% 2.87/2.04 tff(129,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.87/2.04 inference(quant_intro,[status(thm)],[128])).
% 2.87/2.04 tff(130,plain,
% 2.87/2.04 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 2.87/2.04 inference(bind,[status(th)],[])).
% 2.87/2.04 tff(131,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.87/2.04 inference(quant_intro,[status(thm)],[130])).
% 2.87/2.04 tff(132,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.87/2.04 inference(transitivity,[status(thm)],[131, 129])).
% 2.87/2.04 tff(133,plain,
% 2.87/2.04 (^[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) | (~v1_group_1(A)) | (~l1_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)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_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)) | (~l1_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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 2.87/2.04 inference(bind,[status(th)],[])).
% 2.87/2.04 tff(134,plain,
% 2.87/2.04 (![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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.87/2.04 inference(quant_intro,[status(thm)],[133])).
% 2.87/2.04 tff(135,plain,
% 2.87/2.04 (![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), k4_autgroup(A))) | m2_fraenkel(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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(rewrite,[status(thm)],[])).
% 2.87/2.04 tff(136,plain,
% 2.87/2.04 (^[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] : rewrite((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~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), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (((~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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite((((~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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~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), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 2.87/2.04 inference(bind,[status(th)],[])).
% 2.87/2.04 tff(137,plain,
% 2.87/2.04 (![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), k4_autgroup(A)) => m2_fraenkel(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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(quant_intro,[status(thm)],[136])).
% 2.87/2.04 tff(138,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), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_autgroup')).
% 2.87/2.04 tff(139,plain,
% 2.87/2.04 (![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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[138, 137])).
% 2.87/2.04 tff(140,plain,
% 2.87/2.04 (![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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[139, 135])).
% 2.87/2.04 tff(141,plain,(
% 2.87/2.04 ![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), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(skolemize,[status(sab)],[140])).
% 2.87/2.04 tff(142,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[141, 134])).
% 2.87/2.04 tff(143,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[142, 132])).
% 2.87/2.04 tff(144,plain,
% 2.87/2.04 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 2.87/2.04 inference(modus_ponens,[status(thm)],[143, 127])).
% 2.87/2.04 tff(145,plain,
% 2.87/2.04 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 2.87/2.04 inference(rewrite,[status(thm)],[])).
% 2.87/2.04 tff(146,plain,
% 2.87/2.04 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 2.87/2.05 inference(quant_inst,[status(thm)],[])).
% 2.87/2.05 tff(147,plain,
% 2.87/2.05 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 2.87/2.05 inference(modus_ponens,[status(thm)],[146, 145])).
% 2.87/2.05 tff(148,plain,
% 2.87/2.05 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 2.87/2.05 inference(unit_resolution,[status(thm)],[147, 44, 43, 42, 41, 40, 144])).
% 2.87/2.05 tff(149,plain,
% 2.87/2.05 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 2.87/2.05 inference(and_elim,[status(thm)],[39])).
% 2.87/2.05 tff(150,plain,
% 2.87/2.05 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 2.87/2.05 inference(rewrite,[status(thm)],[])).
% 2.87/2.05 tff(151,plain,
% 2.87/2.05 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 2.87/2.05 inference(quant_inst,[status(thm)],[])).
% 2.87/2.05 tff(152,plain,
% 2.87/2.05 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 2.87/2.05 inference(modus_ponens,[status(thm)],[151, 150])).
% 2.87/2.05 tff(153,plain,
% 2.87/2.05 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 2.87/2.05 inference(unit_resolution,[status(thm)],[152, 149, 148])).
% 2.87/2.05 tff(154,plain,
% 2.87/2.05 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))), (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))), rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))), (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))))), (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))))), rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))))),
% 2.87/2.05 inference(bind,[status(th)],[])).
% 2.87/2.05 tff(155,plain,
% 2.87/2.05 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))),
% 2.87/2.05 inference(quant_intro,[status(thm)],[154])).
% 2.87/2.05 tff(156,plain,
% 2.87/2.05 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))),
% 2.87/2.05 inference(bind,[status(th)],[])).
% 2.87/2.05 tff(157,plain,
% 2.87/2.05 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.05 inference(quant_intro,[status(thm)],[156])).
% 2.87/2.05 tff(158,plain,
% 2.87/2.05 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))),
% 2.87/2.05 inference(bind,[status(th)],[])).
% 2.87/2.05 tff(159,plain,
% 2.87/2.05 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.05 inference(quant_intro,[status(thm)],[158])).
% 2.87/2.05 tff(160,plain,
% 2.87/2.05 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.05 inference(transitivity,[status(thm)],[159, 157])).
% 2.87/2.05 tff(161,plain,
% 2.87/2.05 (^[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) | (~v1_group_1(A)) | (~l1_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)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_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)) | (~l1_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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), trans(monotonicity(rewrite(((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) <=> ((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))), trans(monotonicity(rewrite((m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))) <=> (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))), (((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) <=> ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))), rewrite(((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))) <=> ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))), (((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) <=> ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))), ((((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))) <=> (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))), rewrite((((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) <=> (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))), ((((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))) <=> (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, 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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, 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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))))),
% 2.87/2.06 inference(bind,[status(th)],[])).
% 2.87/2.06 tff(162,plain,
% 2.87/2.06 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.06 inference(quant_intro,[status(thm)],[161])).
% 2.87/2.06 tff(163,plain,
% 2.87/2.06 (^[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] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | ((~(~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, 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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.06 inference(bind,[status(th)],[])).
% 2.87/2.06 tff(164,plain,
% 2.87/2.06 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | ((~(~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, 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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))),
% 2.87/2.06 inference(quant_intro,[status(thm)],[163])).
% 2.87/2.06 tff(165,plain,
% 2.87/2.06 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 2.87/2.06 inference(rewrite,[status(thm)],[])).
% 2.87/2.06 tff(166,plain,
% 2.87/2.06 (^[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(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))), rewrite(((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) <=> ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))), (![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), (((((((~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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> (((~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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))), 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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ((~((~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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), (((((((~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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ((~((~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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))),
% 2.87/2.06 inference(bind,[status(th)],[])).
% 2.87/2.06 tff(167,plain,
% 2.87/2.06 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 2.87/2.07 inference(quant_intro,[status(thm)],[166])).
% 2.87/2.07 tff(168,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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_autgroup')).
% 2.87/2.07 tff(169,plain,
% 2.87/2.07 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[168, 167])).
% 2.87/2.07 tff(170,plain,
% 2.87/2.07 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[169, 165])).
% 2.87/2.07 tff(171,plain,(
% 2.87/2.07 ![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | ((~(~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))),
% 2.87/2.07 inference(skolemize,[status(sab)],[170])).
% 2.87/2.07 tff(172,plain,
% 2.87/2.07 (![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, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[171, 164])).
% 2.87/2.07 tff(173,plain,
% 2.87/2.07 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[172, 162])).
% 2.87/2.07 tff(174,plain,
% 2.87/2.07 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[173, 160])).
% 2.87/2.07 tff(175,plain,
% 2.87/2.07 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[174, 155])).
% 2.87/2.07 tff(176,plain,
% 2.87/2.07 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))),
% 2.87/2.07 inference(rewrite,[status(thm)],[])).
% 2.87/2.07 tff(177,plain,
% 2.87/2.07 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))),
% 2.87/2.07 inference(quant_inst,[status(thm)],[])).
% 2.87/2.07 tff(178,plain,
% 2.87/2.07 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))),
% 2.87/2.07 inference(modus_ponens,[status(thm)],[177, 176])).
% 2.87/2.07 tff(179,plain,
% 2.87/2.07 (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))),
% 2.87/2.07 inference(unit_resolution,[status(thm)],[178, 44, 43, 42, 41, 40, 175])).
% 2.87/2.07 tff(180,plain,
% 2.87/2.07 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(181,plain,
% 2.87/2.08 (((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(182,plain,
% 2.87/2.08 ((~(~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(183,plain,
% 2.87/2.08 (($false | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(184,plain,
% 2.87/2.08 ((~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(185,plain,
% 2.87/2.08 ((~$true) <=> $false),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(186,plain,
% 2.87/2.08 (($true | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0)))))) <=> $true),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(187,plain,
% 2.87/2.08 ((k2_autgroup(A!0) = k2_autgroup(A!0)) <=> $true),
% 2.87/2.08 inference(rewrite,[status(thm)],[])).
% 2.87/2.08 tff(188,plain,
% 2.87/2.08 (((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0)))))) <=> ($true | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))),
% 2.87/2.08 inference(monotonicity,[status(thm)],[187])).
% 2.87/2.08 tff(189,plain,
% 2.87/2.08 (((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0)))))) <=> $true),
% 2.87/2.08 inference(transitivity,[status(thm)],[188, 186])).
% 2.87/2.08 tff(190,plain,
% 2.87/2.08 ((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) <=> (~$true)),
% 2.87/2.08 inference(monotonicity,[status(thm)],[189])).
% 2.98/2.08 tff(191,plain,
% 2.98/2.08 ((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) <=> $false),
% 2.98/2.08 inference(transitivity,[status(thm)],[190, 185])).
% 2.98/2.08 tff(192,plain,
% 2.98/2.08 (((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))) <=> ($false | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))),
% 2.98/2.08 inference(monotonicity,[status(thm)],[191, 184])).
% 2.98/2.08 tff(193,plain,
% 2.98/2.08 (((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))) <=> (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.98/2.08 inference(transitivity,[status(thm)],[192, 183])).
% 2.98/2.08 tff(194,plain,
% 2.98/2.08 ((~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) <=> (~(~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))),
% 2.98/2.09 inference(monotonicity,[status(thm)],[193])).
% 2.98/2.09 tff(195,plain,
% 2.98/2.09 ((~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 2.98/2.09 inference(transitivity,[status(thm)],[194, 182])).
% 2.98/2.09 tff(196,plain,
% 2.98/2.09 (((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.98/2.09 inference(monotonicity,[status(thm)],[195])).
% 2.98/2.09 tff(197,plain,
% 2.98/2.09 (((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.98/2.09 inference(transitivity,[status(thm)],[196, 181])).
% 2.98/2.09 tff(198,plain,
% 2.98/2.09 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))),
% 2.99/2.09 inference(monotonicity,[status(thm)],[197])).
% 2.99/2.09 tff(199,plain,
% 2.99/2.09 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 2.99/2.10 inference(transitivity,[status(thm)],[198, 180])).
% 2.99/2.10 tff(200,plain,
% 2.99/2.10 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))),
% 2.99/2.10 inference(quant_inst,[status(thm)],[])).
% 2.99/2.10 tff(201,plain,
% 2.99/2.10 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(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))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 2.99/2.10 inference(modus_ponens,[status(thm)],[200, 199])).
% 2.99/2.10 tff(202,plain,
% 2.99/2.10 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 2.99/2.10 inference(unit_resolution,[status(thm)],[201, 179, 57, 55, 50])).
% 2.99/2.10 tff(203,plain,
% 2.99/2.10 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1))))),
% 2.99/2.10 inference(rewrite,[status(thm)],[])).
% 2.99/2.10 tff(204,plain,
% 2.99/2.10 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1))))),
% 2.99/2.10 inference(quant_inst,[status(thm)],[])).
% 2.99/2.10 tff(205,plain,
% 2.99/2.10 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[204, 203])).
% 3.00/2.11 tff(206,plain,
% 3.00/2.11 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))),
% 3.00/2.11 inference(unit_resolution,[status(thm)],[205, 202, 153])).
% 3.00/2.11 tff(207,plain,
% 3.00/2.11 (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))),
% 3.00/2.11 inference(and_elim,[status(thm)],[39])).
% 3.00/2.11 tff(208,plain,
% 3.00/2.11 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 3.00/2.11 inference(or_elim,[status(thm)],[207])).
% 3.00/2.11 tff(209,plain,
% 3.00/2.11 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(210,plain,
% 3.00/2.11 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 3.00/2.11 inference(quant_inst,[status(thm)],[])).
% 3.00/2.11 tff(211,plain,
% 3.00/2.11 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, 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), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[210, 209])).
% 3.00/2.11 tff(212,plain,
% 3.00/2.11 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 3.00/2.11 inference(unit_resolution,[status(thm)],[211, 208, 148])).
% 3.00/2.11 tff(213,plain,
% 3.00/2.11 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(214,plain,
% 3.00/2.11 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))),
% 3.00/2.11 inference(quant_inst,[status(thm)],[])).
% 3.00/2.11 tff(215,plain,
% 3.00/2.11 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[214, 213])).
% 3.00/2.11 tff(216,plain,
% 3.00/2.11 (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)),
% 3.00/2.11 inference(unit_resolution,[status(thm)],[215, 212, 206])).
% 3.00/2.11 tff(217,plain,
% 3.00/2.11 (((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.11 inference(tautology,[status(thm)],[])).
% 3.00/2.11 tff(218,plain,
% 3.00/2.11 (k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 3.00/2.11 inference(unit_resolution,[status(thm)],[217, 121])).
% 3.00/2.11 tff(219,plain,
% 3.00/2.11 (u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) = k1_autgroup(A!0)),
% 3.00/2.11 inference(symmetry,[status(thm)],[218])).
% 3.00/2.11 tff(220,plain,
% 3.00/2.11 (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2)),
% 3.00/2.11 inference(monotonicity,[status(thm)],[219, 219, 219, 124])).
% 3.00/2.11 tff(221,plain,
% 3.00/2.11 (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)),
% 3.00/2.11 inference(transitivity,[status(thm)],[220, 216])).
% 3.00/2.11 tff(222,plain,
% 3.00/2.11 ((k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) <=> (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k1_binop_1(k2_autgroup(A!0), B!1, C!2))),
% 3.00/2.11 inference(monotonicity,[status(thm)],[221, 125])).
% 3.00/2.11 tff(223,plain,
% 3.00/2.11 ((k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) <=> (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 3.00/2.11 inference(transitivity,[status(thm)],[222, 1])).
% 3.00/2.11 tff(224,plain,
% 3.00/2.11 ((k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)) <=> (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 3.00/2.11 inference(symmetry,[status(thm)],[223])).
% 3.00/2.11 tff(225,plain,
% 3.00/2.11 ((~(k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) <=> (~(k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 3.00/2.11 inference(monotonicity,[status(thm)],[224])).
% 3.00/2.11 tff(226,plain,
% 3.00/2.11 (~(k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 3.00/2.11 inference(or_elim,[status(thm)],[207])).
% 3.00/2.11 tff(227,plain,
% 3.00/2.11 (~(k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[226, 225])).
% 3.00/2.11 tff(228,plain,
% 3.00/2.11 (m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_subset_1(C!2, k1_autgroup(A!0))),
% 3.00/2.11 inference(monotonicity,[status(thm)],[219])).
% 3.00/2.11 tff(229,plain,
% 3.00/2.11 (m1_subset_1(C!2, k1_autgroup(A!0)) <=> m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.11 inference(symmetry,[status(thm)],[228])).
% 3.00/2.11 tff(230,plain,
% 3.00/2.11 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 3.00/2.11 inference(bind,[status(th)],[])).
% 3.00/2.11 tff(231,plain,
% 3.00/2.11 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 3.00/2.11 inference(quant_intro,[status(thm)],[230])).
% 3.00/2.11 tff(232,plain,
% 3.00/2.11 (^[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) | (~v1_group_1(A)) | (~l1_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)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_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)) | (~l1_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) | (~v1_group_1(A)) | (~l1_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) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 3.00/2.11 inference(bind,[status(th)],[])).
% 3.00/2.11 tff(233,plain,
% 3.00/2.11 (![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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 3.00/2.11 inference(quant_intro,[status(thm)],[232])).
% 3.00/2.11 tff(234,plain,
% 3.00/2.11 (![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)))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(235,plain,
% 3.00/2.11 (^[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)))))),
% 3.00/2.11 inference(bind,[status(th)],[])).
% 3.00/2.11 tff(236,plain,
% 3.00/2.11 (![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)))),
% 3.00/2.11 inference(quant_intro,[status(thm)],[235])).
% 3.00/2.11 tff(237,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/sandbox2/benchmark/theBenchmark.p','dt_k1_autgroup')).
% 3.00/2.11 tff(238,plain,
% 3.00/2.11 (![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)))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[237, 236])).
% 3.00/2.11 tff(239,plain,
% 3.00/2.11 (![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)))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[238, 234])).
% 3.00/2.11 tff(240,plain,(
% 3.00/2.11 ![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)))),
% 3.00/2.11 inference(skolemize,[status(sab)],[239])).
% 3.00/2.11 tff(241,plain,
% 3.00/2.11 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[240, 233])).
% 3.00/2.11 tff(242,plain,
% 3.00/2.11 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 3.00/2.11 inference(modus_ponens,[status(thm)],[241, 231])).
% 3.00/2.11 tff(243,plain,
% 3.00/2.11 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(244,plain,
% 3.00/2.11 ((v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(245,plain,
% 3.00/2.11 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A!0)) | (~l1_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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 3.00/2.11 inference(monotonicity,[status(thm)],[244])).
% 3.00/2.11 tff(246,plain,
% 3.00/2.11 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A!0)) | (~l1_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)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 3.00/2.11 inference(transitivity,[status(thm)],[245, 243])).
% 3.00/2.11 tff(247,plain,
% 3.00/2.11 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_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)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(248,plain,
% 3.00/2.12 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[247, 246])).
% 3.00/2.12 tff(249,plain,
% 3.00/2.12 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[248, 44, 43, 42, 41, 40, 242])).
% 3.00/2.12 tff(250,plain,
% 3.00/2.12 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(251,plain,
% 3.00/2.12 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[250])).
% 3.00/2.12 tff(252,plain,
% 3.00/2.12 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(253,plain,
% 3.00/2.12 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(254,plain,
% 3.00/2.12 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[253])).
% 3.00/2.12 tff(255,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 3.00/2.12 tff(256,plain,
% 3.00/2.12 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[255, 254])).
% 3.00/2.12 tff(257,plain,
% 3.00/2.12 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[256, 252])).
% 3.00/2.12 tff(258,plain,(
% 3.00/2.12 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(skolemize,[status(sab)],[257])).
% 3.00/2.12 tff(259,plain,
% 3.00/2.12 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[258, 251])).
% 3.00/2.12 tff(260,plain,
% 3.00/2.12 (((~![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)))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(261,plain,
% 3.00/2.12 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(262,plain,
% 3.00/2.12 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[261, 260])).
% 3.00/2.12 tff(263,plain,
% 3.00/2.12 (l1_struct_0(A!0)),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[262, 40, 259])).
% 3.00/2.12 tff(264,plain,
% 3.00/2.12 (^[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))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(265,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[264])).
% 3.00/2.12 tff(266,plain,
% 3.00/2.12 (^[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)))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(267,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[266])).
% 3.00/2.12 tff(268,plain,
% 3.00/2.12 (![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))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(269,plain,
% 3.00/2.12 (^[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)))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(270,plain,
% 3.00/2.12 (![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))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[269])).
% 3.00/2.12 tff(271,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 3.00/2.12 tff(272,plain,
% 3.00/2.12 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[271, 270])).
% 3.00/2.12 tff(273,plain,
% 3.00/2.12 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[272, 268])).
% 3.00/2.12 tff(274,plain,(
% 3.00/2.12 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.00/2.12 inference(skolemize,[status(sab)],[273])).
% 3.00/2.12 tff(275,plain,
% 3.00/2.12 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[274, 267])).
% 3.00/2.12 tff(276,plain,
% 3.00/2.12 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[275, 265])).
% 3.00/2.12 tff(277,plain,
% 3.00/2.12 (((~![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))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(278,plain,
% 3.00/2.12 ((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))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(279,plain,
% 3.00/2.12 (((~![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)))))),
% 3.00/2.12 inference(monotonicity,[status(thm)],[278])).
% 3.00/2.12 tff(280,plain,
% 3.00/2.12 (((~![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))))),
% 3.00/2.12 inference(transitivity,[status(thm)],[279, 277])).
% 3.00/2.12 tff(281,plain,
% 3.00/2.12 ((~![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)))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(282,plain,
% 3.00/2.12 ((~![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[281, 280])).
% 3.00/2.12 tff(283,plain,
% 3.00/2.12 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[282, 44, 276])).
% 3.00/2.12 tff(284,plain,
% 3.00/2.12 (~v1_xboole_0(u1_struct_0(A!0))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[283, 263])).
% 3.00/2.12 tff(285,plain,
% 3.00/2.12 (^[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))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(286,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[285])).
% 3.00/2.12 tff(287,plain,
% 3.00/2.12 (^[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))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(288,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[287])).
% 3.00/2.12 tff(289,plain,
% 3.00/2.12 (^[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))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(290,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[289])).
% 3.00/2.12 tff(291,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(transitivity,[status(thm)],[290, 288])).
% 3.00/2.12 tff(292,plain,
% 3.00/2.12 (^[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)))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(293,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[292])).
% 3.00/2.12 tff(294,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(295,plain,
% 3.00/2.12 (^[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))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(296,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[295])).
% 3.00/2.12 tff(297,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/sandbox2/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 3.00/2.12 tff(298,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[297, 296])).
% 3.00/2.12 tff(299,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[298, 294])).
% 3.00/2.12 tff(300,plain,(
% 3.00/2.12 ![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)))),
% 3.00/2.12 inference(skolemize,[status(sab)],[299])).
% 3.00/2.12 tff(301,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[300, 293])).
% 3.00/2.12 tff(302,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[301, 291])).
% 3.00/2.12 tff(303,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[302, 286])).
% 3.00/2.12 tff(304,plain,
% 3.00/2.12 (((~![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))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(305,plain,
% 3.00/2.12 ((~![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))))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(306,plain,
% 3.00/2.12 ((~![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)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[305, 304])).
% 3.00/2.12 tff(307,plain,
% 3.00/2.12 (![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)))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[306, 303, 284, 249])).
% 3.00/2.12 tff(308,plain,
% 3.00/2.12 ((~![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)))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(309,plain,
% 3.00/2.12 (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))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[308, 307])).
% 3.00/2.12 tff(310,plain,
% 3.00/2.12 ((~(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))),
% 3.00/2.12 inference(tautology,[status(thm)],[])).
% 3.00/2.12 tff(311,plain,
% 3.00/2.12 ((~(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))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[310, 212])).
% 3.00/2.12 tff(312,plain,
% 3.00/2.12 (m1_subset_1(C!2, k1_autgroup(A!0))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[311, 309])).
% 3.00/2.12 tff(313,plain,
% 3.00/2.12 (m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[312, 229])).
% 3.00/2.12 tff(314,plain,
% 3.00/2.12 (m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_subset_1(B!1, k1_autgroup(A!0))),
% 3.00/2.12 inference(monotonicity,[status(thm)],[219])).
% 3.00/2.12 tff(315,plain,
% 3.00/2.12 (m1_subset_1(B!1, k1_autgroup(A!0)) <=> m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.12 inference(symmetry,[status(thm)],[314])).
% 3.00/2.12 tff(316,plain,
% 3.00/2.12 ((~![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)))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(317,plain,
% 3.00/2.12 (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))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[316, 307])).
% 3.00/2.12 tff(318,plain,
% 3.00/2.12 ((~(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))),
% 3.00/2.12 inference(tautology,[status(thm)],[])).
% 3.00/2.12 tff(319,plain,
% 3.00/2.12 ((~(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))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[318, 153])).
% 3.00/2.12 tff(320,plain,
% 3.00/2.12 (m1_subset_1(B!1, k1_autgroup(A!0))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[319, 317])).
% 3.00/2.12 tff(321,plain,
% 3.00/2.12 (m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[320, 315])).
% 3.00/2.12 tff(322,plain,
% 3.00/2.12 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(323,plain,
% 3.00/2.12 (m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[322, 8])).
% 3.00/2.12 tff(324,plain,
% 3.00/2.12 (^[A: $i] : refl(((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(325,plain,
% 3.00/2.12 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[324])).
% 3.00/2.12 tff(326,plain,
% 3.00/2.12 (^[A: $i] : rewrite(((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(327,plain,
% 3.00/2.12 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[326])).
% 3.00/2.12 tff(328,plain,
% 3.00/2.12 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(329,plain,
% 3.00/2.12 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_group_1(A) => (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_group_1(A) => (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 3.00/2.13 inference(bind,[status(th)],[])).
% 3.00/2.13 tff(330,plain,
% 3.00/2.13 (![A: $i] : (l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.00/2.13 inference(quant_intro,[status(thm)],[329])).
% 3.00/2.13 tff(331,axiom,(![A: $i] : (l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_group_1')).
% 3.00/2.13 tff(332,plain,
% 3.00/2.13 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[331, 330])).
% 3.00/2.13 tff(333,plain,
% 3.00/2.13 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[332, 328])).
% 3.00/2.13 tff(334,plain,(
% 3.00/2.13 ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.00/2.13 inference(skolemize,[status(sab)],[333])).
% 3.00/2.13 tff(335,plain,
% 3.00/2.13 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[334, 327])).
% 3.00/2.13 tff(336,plain,
% 3.00/2.13 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[335, 325])).
% 3.00/2.13 tff(337,plain,
% 3.00/2.13 (((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))) <=> ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(338,plain,
% 3.00/2.13 ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 3.00/2.13 inference(quant_inst,[status(thm)],[])).
% 3.00/2.13 tff(339,plain,
% 3.00/2.13 ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[338, 337])).
% 3.00/2.13 tff(340,plain,
% 3.00/2.13 (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[339, 336, 77])).
% 3.00/2.13 tff(341,plain,
% 3.00/2.13 (((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(tautology,[status(thm)],[])).
% 3.00/2.13 tff(342,plain,
% 3.00/2.13 (m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[341, 340])).
% 3.00/2.13 tff(343,plain,
% 3.00/2.13 ((~(m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(tautology,[status(thm)],[])).
% 3.00/2.13 tff(344,plain,
% 3.00/2.13 ((~(m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[343, 342])).
% 3.00/2.13 tff(345,plain,
% 3.00/2.13 (m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[344, 323])).
% 3.00/2.13 tff(346,plain,
% 3.00/2.13 (((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(tautology,[status(thm)],[])).
% 3.00/2.13 tff(347,plain,
% 3.00/2.13 (v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[346, 340])).
% 3.00/2.13 tff(348,plain,
% 3.00/2.13 (((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(tautology,[status(thm)],[])).
% 3.00/2.13 tff(349,plain,
% 3.00/2.13 (v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[348, 340])).
% 3.00/2.13 tff(350,plain,
% 3.00/2.13 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(351,plain,
% 3.00/2.13 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.13 inference(quant_inst,[status(thm)],[])).
% 3.00/2.13 tff(352,plain,
% 3.00/2.13 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[351, 350])).
% 3.00/2.13 tff(353,plain,
% 3.00/2.13 (l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[352, 259, 77])).
% 3.00/2.13 tff(354,plain,
% 3.00/2.13 (^[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))))))),
% 3.00/2.13 inference(bind,[status(th)],[])).
% 3.00/2.13 tff(355,plain,
% 3.00/2.13 (![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)))))),
% 3.00/2.13 inference(quant_intro,[status(thm)],[354])).
% 3.00/2.13 tff(356,plain,
% 3.00/2.13 (^[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))))))),
% 3.00/2.13 inference(bind,[status(th)],[])).
% 3.00/2.13 tff(357,plain,
% 3.00/2.13 (![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)))))),
% 3.00/2.13 inference(quant_intro,[status(thm)],[356])).
% 3.00/2.13 tff(358,plain,
% 3.00/2.13 (![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)))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(359,plain,
% 3.00/2.13 (^[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))))),
% 3.00/2.13 inference(bind,[status(th)],[])).
% 3.00/2.13 tff(360,plain,
% 3.00/2.13 (![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)))),
% 3.00/2.13 inference(quant_intro,[status(thm)],[359])).
% 3.00/2.13 tff(361,axiom,(![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_fraenkel')).
% 3.00/2.13 tff(362,plain,
% 3.00/2.13 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[361, 360])).
% 3.00/2.13 tff(363,plain,
% 3.00/2.13 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[362, 358])).
% 3.00/2.13 tff(364,plain,(
% 3.00/2.13 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 3.00/2.13 inference(skolemize,[status(sab)],[363])).
% 3.00/2.13 tff(365,plain,
% 3.00/2.13 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[364, 357])).
% 3.00/2.13 tff(366,plain,
% 3.00/2.13 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[365, 355])).
% 3.00/2.13 tff(367,plain,
% 3.00/2.13 (((~![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))))))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(368,plain,
% 3.00/2.13 ((~![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))))))),
% 3.00/2.13 inference(quant_inst,[status(thm)],[])).
% 3.00/2.13 tff(369,plain,
% 3.00/2.13 ((~![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)))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[368, 367])).
% 3.00/2.13 tff(370,plain,
% 3.00/2.13 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[369, 366, 249])).
% 3.00/2.13 tff(371,plain,
% 3.00/2.13 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 3.00/2.13 inference(tautology,[status(thm)],[])).
% 3.00/2.13 tff(372,plain,
% 3.00/2.13 (~v1_xboole_0(k1_autgroup(A!0))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[371, 370])).
% 3.00/2.13 tff(373,plain,
% 3.00/2.13 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))))),
% 3.00/2.13 inference(bind,[status(th)],[])).
% 3.00/2.13 tff(374,plain,
% 3.00/2.13 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 3.00/2.13 inference(quant_intro,[status(thm)],[373])).
% 3.00/2.13 tff(375,plain,
% 3.00/2.13 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), rewrite(((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))) <=> (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))), (((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ((v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))), (((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))))),
% 3.00/2.14 inference(bind,[status(th)],[])).
% 3.00/2.14 tff(376,plain,
% 3.00/2.14 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 3.00/2.14 inference(quant_intro,[status(thm)],[375])).
% 3.00/2.14 tff(377,plain,
% 3.00/2.14 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 3.00/2.14 inference(rewrite,[status(thm)],[])).
% 3.00/2.14 tff(378,plain,
% 3.00/2.14 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A))), (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> (((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))), ((((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))))),
% 3.00/2.14 inference(bind,[status(th)],[])).
% 3.00/2.14 tff(379,plain,
% 3.00/2.14 (![A: $i, B: $i] : (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 3.00/2.14 inference(quant_intro,[status(thm)],[378])).
% 3.00/2.14 tff(380,axiom,(![A: $i, B: $i] : (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_group_1')).
% 3.00/2.14 tff(381,plain,
% 3.00/2.14 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 3.00/2.14 inference(modus_ponens,[status(thm)],[380, 379])).
% 3.00/2.14 tff(382,plain,
% 3.00/2.14 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 3.00/2.14 inference(modus_ponens,[status(thm)],[381, 377])).
% 3.00/2.14 tff(383,plain,(
% 3.00/2.14 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 3.00/2.14 inference(skolemize,[status(sab)],[382])).
% 3.00/2.14 tff(384,plain,
% 3.00/2.14 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 3.00/2.14 inference(modus_ponens,[status(thm)],[383, 376])).
% 3.00/2.14 tff(385,plain,
% 3.00/2.14 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 3.00/2.14 inference(modus_ponens,[status(thm)],[384, 374])).
% 3.00/2.14 tff(386,plain,
% 3.00/2.14 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 3.00/2.14 inference(rewrite,[status(thm)],[])).
% 3.00/2.14 tff(387,plain,
% 3.00/2.14 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 3.00/2.14 inference(rewrite,[status(thm)],[])).
% 3.00/2.14 tff(388,plain,
% 3.00/2.14 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 3.00/2.14 inference(monotonicity,[status(thm)],[387])).
% 3.00/2.14 tff(389,plain,
% 3.00/2.14 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 3.00/2.14 inference(transitivity,[status(thm)],[388, 386])).
% 3.00/2.14 tff(390,plain,
% 3.00/2.14 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 3.00/2.14 inference(quant_inst,[status(thm)],[])).
% 3.00/2.14 tff(391,plain,
% 3.00/2.14 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.14 inference(modus_ponens,[status(thm)],[390, 389])).
% 3.00/2.14 tff(392,plain,
% 3.00/2.14 ((~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.14 inference(unit_resolution,[status(thm)],[391, 385, 57, 55])).
% 3.00/2.14 tff(393,plain,
% 3.00/2.14 (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.14 inference(unit_resolution,[status(thm)],[392, 372, 53])).
% 3.00/2.14 tff(394,plain,
% 3.00/2.14 ((v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.14 inference(tautology,[status(thm)],[])).
% 3.00/2.14 tff(395,plain,
% 3.00/2.14 (~v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 3.00/2.14 inference(unit_resolution,[status(thm)],[394, 393])).
% 3.00/2.14 tff(396,plain,
% 3.00/2.14 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.14 inference(rewrite,[status(thm)],[])).
% 3.00/2.14 tff(397,plain,
% 3.00/2.14 ((v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) <=> (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.14 inference(rewrite,[status(thm)],[])).
% 3.00/2.14 tff(398,plain,
% 3.00/2.14 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 3.00/2.14 inference(monotonicity,[status(thm)],[397])).
% 3.00/2.14 tff(399,plain,
% 3.00/2.14 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.14 inference(transitivity,[status(thm)],[398, 396])).
% 3.00/2.14 tff(400,plain,
% 3.00/2.14 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.14 inference(quant_inst,[status(thm)],[])).
% 3.00/2.14 tff(401,plain,
% 3.00/2.14 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.14 inference(modus_ponens,[status(thm)],[400, 399])).
% 3.00/2.14 tff(402,plain,
% 3.00/2.14 ((~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 3.00/2.14 inference(unit_resolution,[status(thm)],[401, 276, 395])).
% 3.00/2.14 tff(403,plain,
% 3.00/2.14 (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 3.00/2.14 inference(unit_resolution,[status(thm)],[402, 353])).
% 3.00/2.14 tff(404,plain,
% 3.00/2.14 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))),
% 3.00/2.14 inference(bind,[status(th)],[])).
% 3.00/2.14 tff(405,plain,
% 3.00/2.14 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.00/2.14 inference(quant_intro,[status(thm)],[404])).
% 3.00/2.14 tff(406,plain,
% 3.00/2.14 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) <=> (~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))))), rewrite((~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))))), rewrite(((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))))),
% 3.00/2.14 inference(bind,[status(th)],[])).
% 3.00/2.14 tff(407,plain,
% 3.00/2.14 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.00/2.15 inference(quant_intro,[status(thm)],[406])).
% 3.00/2.15 tff(408,plain,
% 3.00/2.15 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 3.00/2.15 inference(rewrite,[status(thm)],[])).
% 3.00/2.15 tff(409,plain,
% 3.00/2.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))))),
% 3.00/2.15 inference(bind,[status(th)],[])).
% 3.00/2.15 tff(410,plain,
% 3.00/2.15 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 3.00/2.15 inference(quant_intro,[status(thm)],[409])).
% 3.00/2.15 tff(411,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_binop_1')).
% 3.00/2.15 tff(412,plain,
% 3.00/2.15 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 3.00/2.15 inference(modus_ponens,[status(thm)],[411, 410])).
% 3.00/2.15 tff(413,plain,
% 3.00/2.15 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 3.00/2.15 inference(modus_ponens,[status(thm)],[412, 408])).
% 3.00/2.15 tff(414,plain,(
% 3.00/2.15 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 3.00/2.15 inference(skolemize,[status(sab)],[413])).
% 3.00/2.15 tff(415,plain,
% 3.00/2.15 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.00/2.15 inference(modus_ponens,[status(thm)],[414, 407])).
% 3.00/2.15 tff(416,plain,
% 3.00/2.15 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.00/2.15 inference(modus_ponens,[status(thm)],[415, 405])).
% 3.00/2.15 tff(417,plain,
% 3.00/2.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 3.00/2.15 inference(rewrite,[status(thm)],[])).
% 3.00/2.15 tff(418,plain,
% 3.00/2.15 ((v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 3.00/2.15 inference(rewrite,[status(thm)],[])).
% 3.00/2.15 tff(419,plain,
% 3.00/2.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))))),
% 3.00/2.15 inference(monotonicity,[status(thm)],[418])).
% 3.00/2.15 tff(420,plain,
% 3.00/2.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 3.00/2.16 inference(transitivity,[status(thm)],[419, 417])).
% 3.00/2.16 tff(421,plain,
% 3.00/2.16 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 3.00/2.18 inference(quant_inst,[status(thm)],[])).
% 3.00/2.18 tff(422,plain,
% 3.00/2.18 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 3.00/2.18 inference(modus_ponens,[status(thm)],[421, 420])).
% 3.00/2.18 tff(423,plain,
% 3.00/2.18 ((~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 3.00/2.18 inference(unit_resolution,[status(thm)],[422, 416, 403, 349, 347, 345])).
% 3.00/2.18 tff(424,plain,
% 3.00/2.18 ($false),
% 3.00/2.18 inference(unit_resolution,[status(thm)],[423, 321, 313, 227])).
% 3.00/2.18 % SZS output end Proof
%------------------------------------------------------------------------------