TSTP Solution File: GRP630+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP630+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 22:28:58 EDT 2022
% Result : Theorem 182.03s 115.69s
% Output : Proof 182.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP630+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 18:49:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 182.03/115.69 % SZS status Theorem
% 182.03/115.69 % SZS output start Proof
% 182.03/115.69 tff(v1_xboole_0_type, type, (
% 182.03/115.69 v1_xboole_0: $i > $o)).
% 182.03/115.69 tff(u1_struct_0_type, type, (
% 182.03/115.69 u1_struct_0: $i > $i)).
% 182.03/115.69 tff(tptp_fun_A_0_type, type, (
% 182.03/115.69 tptp_fun_A_0: $i)).
% 182.03/115.69 tff(k1_xboole_0_type, type, (
% 182.03/115.69 k1_xboole_0: $i)).
% 182.03/115.69 tff(k6_partfun1_type, type, (
% 182.03/115.69 k6_partfun1: $i > $i)).
% 182.03/115.69 tff(k1_partfun1_type, type, (
% 182.03/115.69 k1_partfun1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 182.03/115.69 tff(k6_autgroup_type, type, (
% 182.03/115.69 k6_autgroup: ( $i * $i ) > $i)).
% 182.03/115.69 tff(k3_group_1_type, type, (
% 182.03/115.69 k3_group_1: ( $i * $i ) > $i)).
% 182.03/115.69 tff(tptp_fun_B_1_type, type, (
% 182.03/115.69 tptp_fun_B_1: $i)).
% 182.03/115.69 tff(k2_group_1_type, type, (
% 182.03/115.69 k2_group_1: $i > $i)).
% 182.03/115.69 tff(v4_group_1_type, type, (
% 182.03/115.69 v4_group_1: $i > $o)).
% 182.03/115.69 tff(v3_group_1_type, type, (
% 182.03/115.69 v3_group_1: $i > $o)).
% 182.03/115.69 tff(l1_group_1_type, type, (
% 182.03/115.69 l1_group_1: $i > $o)).
% 182.03/115.69 tff(v1_group_1_type, type, (
% 182.03/115.69 v1_group_1: $i > $o)).
% 182.03/115.69 tff(v3_struct_0_type, type, (
% 182.03/115.69 v3_struct_0: $i > $o)).
% 182.03/115.69 tff(k2_funct_1_type, type, (
% 182.03/115.69 k2_funct_1: $i > $i)).
% 182.03/115.69 tff(m1_subset_1_type, type, (
% 182.03/115.69 m1_subset_1: ( $i * $i ) > $o)).
% 182.03/115.70 tff(k7_funct_2_type, type, (
% 182.03/115.70 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 182.03/115.70 tff(k5_relat_1_type, type, (
% 182.03/115.70 k5_relat_1: ( $i * $i ) > $i)).
% 182.03/115.70 tff(m1_relset_1_type, type, (
% 182.03/115.70 m1_relset_1: ( $i * $i * $i ) > $o)).
% 182.03/115.70 tff(m2_relset_1_type, type, (
% 182.03/115.70 m2_relset_1: ( $i * $i * $i ) > $o)).
% 182.03/115.70 tff(v1_group_6_type, type, (
% 182.03/115.70 v1_group_6: ( $i * $i * $i ) > $o)).
% 182.03/115.70 tff(v1_funct_2_type, type, (
% 182.03/115.70 v1_funct_2: ( $i * $i * $i ) > $o)).
% 182.03/115.70 tff(v1_funct_1_type, type, (
% 182.03/115.70 v1_funct_1: $i > $o)).
% 182.03/115.70 tff(m2_fraenkel_type, type, (
% 182.03/115.70 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 182.03/115.70 tff(k1_autgroup_type, type, (
% 182.03/115.70 k1_autgroup: $i > $i)).
% 182.03/115.70 tff(k4_autgroup_type, type, (
% 182.03/115.70 k4_autgroup: $i > $i)).
% 182.03/115.70 tff(v3_group_6_type, type, (
% 182.03/115.70 v3_group_6: ( $i * $i * $i ) > $o)).
% 182.03/115.70 tff(v2_funct_1_type, type, (
% 182.03/115.70 v2_funct_1: $i > $o)).
% 182.03/115.70 tff(r2_hidden_type, type, (
% 182.03/115.70 r2_hidden: ( $i * $i ) > $o)).
% 182.03/115.70 tff(tptp_fun_C_3_type, type, (
% 182.03/115.70 tptp_fun_C_3: ( $i * $i ) > $i)).
% 182.03/115.70 tff(tptp_fun_C_2_type, type, (
% 182.03/115.70 tptp_fun_C_2: ( $i * $i ) > $i)).
% 182.03/115.70 tff(m1_fraenkel_type, type, (
% 182.03/115.70 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 182.03/115.70 tff(l1_struct_0_type, type, (
% 182.03/115.70 l1_struct_0: $i > $o)).
% 182.03/115.70 tff(k2_relat_1_type, type, (
% 182.03/115.70 k2_relat_1: $i > $i)).
% 182.03/115.70 tff(k1_relat_1_type, type, (
% 182.03/115.70 k1_relat_1: $i > $i)).
% 182.03/115.70 tff(v1_fraenkel_type, type, (
% 182.03/115.70 v1_fraenkel: $i > $o)).
% 182.03/115.70 tff(1,plain,
% 182.03/115.70 (^[A: $i] : refl((v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(2,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[1])).
% 182.03/115.70 tff(3,plain,
% 182.03/115.70 (^[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))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(4,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[3])).
% 182.03/115.70 tff(5,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(6,plain,
% 182.03/115.70 (^[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)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(7,plain,
% 182.03/115.70 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[6])).
% 182.03/115.70 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_autgroup')).
% 182.03/115.70 tff(9,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[8, 7])).
% 182.03/115.70 tff(10,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[9, 5])).
% 182.03/115.70 tff(11,plain,(
% 182.03/115.70 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 182.03/115.70 inference(skolemize,[status(sab)],[10])).
% 182.03/115.70 tff(12,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[11, 4])).
% 182.03/115.70 tff(13,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[12, 2])).
% 182.03/115.70 tff(14,plain,
% 182.03/115.70 ((((~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)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, 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) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(15,plain,
% 182.03/115.70 ((~(~((~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))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(16,plain,
% 182.03/115.70 (((~(~((~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)))) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, 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)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))))))),
% 182.03/115.70 inference(monotonicity,[status(thm)],[15])).
% 182.03/115.70 tff(17,plain,
% 182.03/115.70 (((~(~((~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)))) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, 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) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))))))),
% 182.03/115.70 inference(transitivity,[status(thm)],[16, 14])).
% 182.03/115.70 tff(18,plain,
% 182.03/115.70 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, 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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B))))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(19,plain,
% 182.03/115.70 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, 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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B))))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(20,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_autgroup')).
% 182.03/115.70 tff(21,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[20, 19])).
% 182.03/115.70 tff(22,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[21, 18])).
% 182.03/115.70 tff(23,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[22, 18])).
% 182.03/115.70 tff(24,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[23, 18])).
% 182.03/115.70 tff(25,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[24, 18])).
% 182.03/115.70 tff(26,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[25, 18])).
% 182.03/115.70 tff(27,plain,
% 182.03/115.70 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[26, 18])).
% 182.03/115.70 tff(28,plain,
% 182.03/115.70 ((~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) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[27, 17])).
% 182.03/115.70 tff(29,plain,
% 182.03/115.70 (l1_group_1(A!0)),
% 182.03/115.70 inference(and_elim,[status(thm)],[28])).
% 182.03/115.70 tff(30,plain,
% 182.03/115.70 (v4_group_1(A!0)),
% 182.03/115.70 inference(and_elim,[status(thm)],[28])).
% 182.03/115.70 tff(31,plain,
% 182.03/115.70 (v3_group_1(A!0)),
% 182.03/115.70 inference(and_elim,[status(thm)],[28])).
% 182.03/115.70 tff(32,plain,
% 182.03/115.70 (v1_group_1(A!0)),
% 182.03/115.70 inference(and_elim,[status(thm)],[28])).
% 182.03/115.70 tff(33,plain,
% 182.03/115.70 (~v3_struct_0(A!0)),
% 182.03/115.70 inference(and_elim,[status(thm)],[28])).
% 182.03/115.70 tff(34,plain,
% 182.03/115.70 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(35,plain,
% 182.03/115.70 ((v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(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)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(36,plain,
% 182.03/115.70 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(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) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.70 inference(monotonicity,[status(thm)],[35])).
% 182.03/115.70 tff(37,plain,
% 182.03/115.70 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(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) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))),
% 182.03/115.70 inference(transitivity,[status(thm)],[36, 34])).
% 182.03/115.70 tff(38,plain,
% 182.03/115.70 ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(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)))),
% 182.03/115.70 inference(quant_inst,[status(thm)],[])).
% 182.03/115.70 tff(39,plain,
% 182.03/115.70 ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(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)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[38, 37])).
% 182.03/115.70 tff(40,plain,
% 182.03/115.70 (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 182.03/115.70 inference(unit_resolution,[status(thm)],[39, 33, 32, 31, 30, 29, 13])).
% 182.03/115.70 tff(41,plain,
% 182.03/115.70 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(42,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[41])).
% 182.03/115.70 tff(43,plain,
% 182.03/115.70 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(44,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[43])).
% 182.03/115.70 tff(45,plain,
% 182.03/115.70 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(46,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[45])).
% 182.03/115.70 tff(47,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(transitivity,[status(thm)],[46, 44])).
% 182.03/115.70 tff(48,plain,
% 182.03/115.70 (^[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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(49,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[48])).
% 182.03/115.70 tff(50,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(51,plain,
% 182.03/115.70 (^[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((m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(52,plain,
% 182.03/115.70 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[51])).
% 182.03/115.70 tff(53,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_autgroup')).
% 182.03/115.70 tff(54,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[53, 52])).
% 182.03/115.70 tff(55,plain,
% 182.03/115.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[54, 50])).
% 182.03/115.70 tff(56,plain,(
% 182.03/115.70 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(skolemize,[status(sab)],[55])).
% 182.03/115.70 tff(57,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[56, 49])).
% 182.03/115.70 tff(58,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[57, 47])).
% 182.03/115.70 tff(59,plain,
% 182.03/115.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[58, 42])).
% 182.03/115.70 tff(60,plain,
% 182.03/115.70 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(61,plain,
% 182.03/115.70 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))))),
% 182.03/115.70 inference(quant_inst,[status(thm)],[])).
% 182.03/115.70 tff(62,plain,
% 182.03/115.70 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_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)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[61, 60])).
% 182.03/115.70 tff(63,plain,
% 182.03/115.70 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 182.03/115.70 inference(unit_resolution,[status(thm)],[62, 33, 32, 31, 30, 29, 59])).
% 182.03/115.70 tff(64,plain,
% 182.03/115.70 (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))))),
% 182.03/115.70 inference(and_elim,[status(thm)],[28])).
% 182.03/115.70 tff(65,plain,
% 182.03/115.70 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 182.03/115.70 inference(or_elim,[status(thm)],[64])).
% 182.03/115.70 tff(66,plain,
% 182.03/115.70 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(67,plain,
% 182.03/115.70 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 182.03/115.70 inference(quant_inst,[status(thm)],[])).
% 182.03/115.70 tff(68,plain,
% 182.03/115.70 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[67, 66])).
% 182.03/115.70 tff(69,plain,
% 182.03/115.70 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))),
% 182.03/115.70 inference(unit_resolution,[status(thm)],[68, 65, 63])).
% 182.03/115.70 tff(70,plain,
% 182.03/115.70 (^[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)))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(71,plain,
% 182.03/115.70 (![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))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[70])).
% 182.03/115.70 tff(72,plain,
% 182.03/115.70 (![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))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(73,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')).
% 182.03/115.70 tff(74,plain,
% 182.03/115.70 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[73, 72])).
% 182.03/115.70 tff(75,plain,(
% 182.03/115.70 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 182.03/115.70 inference(skolemize,[status(sab)],[74])).
% 182.03/115.70 tff(76,plain,
% 182.03/115.70 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[75, 71])).
% 182.03/115.70 tff(77,plain,
% 182.03/115.70 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 182.03/115.70 inference(quant_inst,[status(thm)],[])).
% 182.03/115.70 tff(78,plain,
% 182.03/115.70 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.70 inference(unit_resolution,[status(thm)],[77, 76])).
% 182.03/115.70 tff(79,plain,
% 182.03/115.70 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(80,plain,
% 182.03/115.70 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[79])).
% 182.03/115.70 tff(81,plain,
% 182.03/115.70 (^[A: $i, B: $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) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(82,plain,
% 182.03/115.70 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[81])).
% 182.03/115.70 tff(83,plain,
% 182.03/115.70 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 182.03/115.70 inference(rewrite,[status(thm)],[])).
% 182.03/115.70 tff(84,plain,
% 182.03/115.70 (^[A: $i, B: $i] : trans(monotonicity(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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), ((((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))))),
% 182.03/115.70 inference(bind,[status(th)],[])).
% 182.03/115.70 tff(85,plain,
% 182.03/115.70 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 182.03/115.70 inference(quant_intro,[status(thm)],[84])).
% 182.03/115.70 tff(86,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_autgroup')).
% 182.03/115.70 tff(87,plain,
% 182.03/115.70 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[86, 85])).
% 182.03/115.70 tff(88,plain,
% 182.03/115.70 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[87, 83])).
% 182.03/115.70 tff(89,plain,(
% 182.03/115.70 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 182.03/115.70 inference(skolemize,[status(sab)],[88])).
% 182.03/115.70 tff(90,plain,
% 182.03/115.70 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[89, 82])).
% 182.03/115.70 tff(91,plain,
% 182.03/115.70 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 182.03/115.70 inference(modus_ponens,[status(thm)],[90, 80])).
% 182.03/115.70 tff(92,plain,
% 182.03/115.70 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~m1_subset_1(B!1, u1_struct_0(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)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~m1_subset_1(B!1, u1_struct_0(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)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 182.03/115.71 inference(rewrite,[status(thm)],[])).
% 182.03/115.71 tff(93,plain,
% 182.03/115.71 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(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)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 182.03/115.71 inference(rewrite,[status(thm)],[])).
% 182.03/115.71 tff(94,plain,
% 182.03/115.71 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~m1_subset_1(B!1, u1_struct_0(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)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))))),
% 182.03/115.71 inference(monotonicity,[status(thm)],[93])).
% 182.03/115.71 tff(95,plain,
% 182.03/115.71 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~m1_subset_1(B!1, u1_struct_0(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)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 182.03/115.71 inference(transitivity,[status(thm)],[94, 92])).
% 182.03/115.71 tff(96,plain,
% 182.03/115.71 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 182.03/115.71 inference(quant_inst,[status(thm)],[])).
% 182.03/115.71 tff(97,plain,
% 182.03/115.71 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~m1_subset_1(B!1, u1_struct_0(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)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[96, 95])).
% 182.03/115.71 tff(98,plain,
% 182.03/115.71 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 182.03/115.71 inference(unit_resolution,[status(thm)],[97, 33, 32, 31, 30, 29, 65, 91])).
% 182.03/115.71 tff(99,plain,
% 182.03/115.71 (^[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)))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(100,plain,
% 182.03/115.71 (![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))))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[99])).
% 182.03/115.71 tff(101,plain,
% 182.03/115.71 (^[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))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(102,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[101])).
% 182.03/115.71 tff(103,plain,
% 182.03/115.71 (^[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))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(104,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[103])).
% 182.03/115.71 tff(105,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(transitivity,[status(thm)],[104, 102])).
% 182.03/115.71 tff(106,plain,
% 182.03/115.71 (^[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)))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(107,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[106])).
% 182.03/115.71 tff(108,plain,
% 182.03/115.71 (![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))))),
% 182.03/115.71 inference(rewrite,[status(thm)],[])).
% 182.03/115.71 tff(109,plain,
% 182.03/115.71 (^[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))))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(110,plain,
% 182.03/115.71 (![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))))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[109])).
% 182.03/115.71 tff(111,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')).
% 182.03/115.71 tff(112,plain,
% 182.03/115.71 (![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))))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[111, 110])).
% 182.03/115.71 tff(113,plain,
% 182.03/115.71 (![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))))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[112, 108])).
% 182.03/115.71 tff(114,plain,(
% 182.03/115.71 ![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))))),
% 182.03/115.71 inference(skolemize,[status(sab)],[113])).
% 182.03/115.71 tff(115,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[114, 107])).
% 182.03/115.71 tff(116,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[115, 105])).
% 182.03/115.71 tff(117,plain,
% 182.03/115.71 (![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))))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[116, 100])).
% 182.03/115.71 tff(118,plain,
% 182.03/115.71 (((~![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))))),
% 182.03/115.71 inference(rewrite,[status(thm)],[])).
% 182.03/115.71 tff(119,plain,
% 182.03/115.71 ((~![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))))),
% 182.03/115.71 inference(quant_inst,[status(thm)],[])).
% 182.03/115.71 tff(120,plain,
% 182.03/115.71 ((~![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)))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[119, 118])).
% 182.03/115.71 tff(121,plain,
% 182.03/115.71 (![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)))),
% 182.03/115.71 inference(unit_resolution,[status(thm)],[120, 33, 32, 31, 30, 29, 117])).
% 182.03/115.71 tff(122,plain,
% 182.03/115.71 (((~![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(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, 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(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 182.03/115.71 inference(rewrite,[status(thm)],[])).
% 182.03/115.71 tff(123,plain,
% 182.03/115.71 ((~![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(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 182.03/115.71 inference(quant_inst,[status(thm)],[])).
% 182.03/115.71 tff(124,plain,
% 182.03/115.71 ((~![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(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 182.03/115.71 inference(modus_ponens,[status(thm)],[123, 122])).
% 182.03/115.71 tff(125,plain,
% 182.03/115.71 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 182.03/115.71 inference(unit_resolution,[status(thm)],[124, 121, 98])).
% 182.03/115.71 tff(126,plain,
% 182.03/115.71 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))))))))), rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(127,plain,
% 182.03/115.71 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, 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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[126])).
% 182.03/115.71 tff(128,plain,
% 182.03/115.71 (^[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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(129,plain,
% 182.03/115.71 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, 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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[128])).
% 182.03/115.71 tff(130,plain,
% 182.03/115.71 (^[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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(131,plain,
% 182.03/115.71 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, 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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[130])).
% 182.03/115.71 tff(132,plain,
% 182.03/115.71 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, 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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))),
% 182.03/115.71 inference(transitivity,[status(thm)],[131, 129])).
% 182.03/115.71 tff(133,plain,
% 182.03/115.71 (^[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] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))))),
% 182.03/115.71 inference(bind,[status(th)],[])).
% 182.03/115.71 tff(134,plain,
% 182.03/115.71 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, 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] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))),
% 182.03/115.71 inference(quant_intro,[status(thm)],[133])).
% 182.03/115.71 tff(135,plain,
% 182.03/115.71 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))),
% 182.03/115.72 inference(bind,[status(th)],[])).
% 182.03/115.72 tff(136,plain,
% 182.03/115.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))),
% 182.03/115.72 inference(quant_intro,[status(thm)],[135])).
% 182.03/115.72 tff(137,plain,
% 182.03/115.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 182.03/115.72 inference(rewrite,[status(thm)],[])).
% 182.03/115.72 tff(138,plain,
% 182.03/115.72 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) <=> ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), rewrite((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), (![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))))),
% 182.03/115.72 inference(bind,[status(th)],[])).
% 182.03/115.72 tff(139,plain,
% 182.03/115.72 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 182.03/115.72 inference(quant_intro,[status(thm)],[138])).
% 182.03/115.72 tff(140,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_autgroup')).
% 182.03/115.72 tff(141,plain,
% 182.03/115.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[140, 139])).
% 182.03/115.72 tff(142,plain,
% 182.03/115.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[141, 137])).
% 182.03/115.72 tff(143,plain,(
% 182.03/115.72 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))),
% 182.03/115.72 inference(skolemize,[status(sab)],[142])).
% 182.03/115.72 tff(144,plain,
% 182.03/115.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[143, 136])).
% 182.03/115.72 tff(145,plain,
% 182.03/115.72 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[144, 134])).
% 182.03/115.72 tff(146,plain,
% 182.03/115.72 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[145, 132])).
% 182.03/115.72 tff(147,plain,
% 182.03/115.72 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[146, 127])).
% 182.03/115.72 tff(148,plain,
% 182.03/115.72 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))))),
% 182.03/115.72 inference(rewrite,[status(thm)],[])).
% 182.03/115.72 tff(149,plain,
% 182.03/115.72 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))))),
% 182.03/115.72 inference(quant_inst,[status(thm)],[])).
% 182.03/115.72 tff(150,plain,
% 182.03/115.72 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[149, 148])).
% 182.03/115.72 tff(151,plain,
% 182.03/115.72 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))),
% 182.03/115.72 inference(unit_resolution,[status(thm)],[150, 33, 32, 31, 30, 29, 147])).
% 182.03/115.72 tff(152,plain,
% 182.03/115.72 (^[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))))),
% 182.03/115.72 inference(bind,[status(th)],[])).
% 182.03/115.72 tff(153,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(quant_intro,[status(thm)],[152])).
% 182.03/115.72 tff(154,plain,
% 182.03/115.72 (^[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)))))),
% 182.03/115.72 inference(bind,[status(th)],[])).
% 182.03/115.72 tff(155,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(quant_intro,[status(thm)],[154])).
% 182.03/115.72 tff(156,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(rewrite,[status(thm)],[])).
% 182.03/115.72 tff(157,plain,
% 182.03/115.72 (^[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)))))),
% 182.03/115.72 inference(bind,[status(th)],[])).
% 182.03/115.72 tff(158,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(quant_intro,[status(thm)],[157])).
% 182.03/115.72 tff(159,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')).
% 182.03/115.72 tff(160,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[159, 158])).
% 182.03/115.72 tff(161,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[160, 156])).
% 182.03/115.72 tff(162,plain,(
% 182.03/115.72 ![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)))),
% 182.03/115.72 inference(skolemize,[status(sab)],[161])).
% 182.03/115.72 tff(163,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[162, 155])).
% 182.03/115.72 tff(164,plain,
% 182.03/115.72 (![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)))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[163, 153])).
% 182.03/115.72 tff(165,plain,
% 182.03/115.72 (((~![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)))),
% 182.03/115.72 inference(rewrite,[status(thm)],[])).
% 182.03/115.72 tff(166,plain,
% 182.03/115.72 ((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)))),
% 182.03/115.72 inference(rewrite,[status(thm)],[])).
% 182.03/115.72 tff(167,plain,
% 182.03/115.72 (((~![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))))),
% 182.03/115.72 inference(monotonicity,[status(thm)],[166])).
% 182.03/115.72 tff(168,plain,
% 182.03/115.72 (((~![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)))),
% 182.03/115.72 inference(transitivity,[status(thm)],[167, 165])).
% 182.03/115.72 tff(169,plain,
% 182.03/115.72 ((~![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)))),
% 182.03/115.72 inference(quant_inst,[status(thm)],[])).
% 182.03/115.72 tff(170,plain,
% 182.03/115.72 ((~![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))),
% 182.03/115.72 inference(modus_ponens,[status(thm)],[169, 168])).
% 182.03/115.72 tff(171,plain,
% 182.03/115.72 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.72 inference(unit_resolution,[status(thm)],[170, 33, 32, 31, 30, 29, 164])).
% 182.03/115.72 tff(172,plain,
% 182.03/115.72 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))),
% 182.03/115.72 inference(rewrite,[status(thm)],[])).
% 182.03/115.72 tff(173,plain,
% 182.03/115.72 (((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))) <=> ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))),
% 182.03/115.73 inference(rewrite,[status(thm)],[])).
% 182.03/115.73 tff(174,plain,
% 182.03/115.73 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))),
% 182.03/115.73 inference(monotonicity,[status(thm)],[173])).
% 182.03/115.73 tff(175,plain,
% 182.03/115.73 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))),
% 182.03/115.73 inference(transitivity,[status(thm)],[174, 172])).
% 182.03/115.73 tff(176,plain,
% 182.03/115.73 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))),
% 182.03/115.73 inference(quant_inst,[status(thm)],[])).
% 182.03/115.73 tff(177,plain,
% 182.03/115.73 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_3(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))),
% 182.03/115.73 inference(modus_ponens,[status(thm)],[176, 175])).
% 182.03/115.73 tff(178,plain,
% 182.03/115.73 (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[177, 171, 151])).
% 182.03/115.73 tff(179,plain,
% 182.03/115.73 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 182.03/115.73 inference(tautology,[status(thm)],[])).
% 182.03/115.73 tff(180,plain,
% 182.03/115.73 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[179, 178])).
% 182.03/115.73 tff(181,plain,
% 182.03/115.73 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 182.03/115.73 inference(rewrite,[status(thm)],[])).
% 182.03/115.73 tff(182,plain,
% 182.03/115.73 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 182.03/115.73 inference(quant_inst,[status(thm)],[])).
% 182.03/115.73 tff(183,plain,
% 182.03/115.73 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 182.03/115.73 inference(modus_ponens,[status(thm)],[182, 181])).
% 182.03/115.73 tff(184,plain,
% 182.03/115.73 (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[183, 180, 125])).
% 182.03/115.73 tff(185,plain,
% 182.03/115.73 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(tautology,[status(thm)],[])).
% 182.03/115.73 tff(186,plain,
% 182.03/115.73 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[185, 184])).
% 182.03/115.73 tff(187,plain,
% 182.03/115.73 ((~(m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(tautology,[status(thm)],[])).
% 182.03/115.73 tff(188,plain,
% 182.03/115.73 ((~(m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[187, 186])).
% 182.03/115.73 tff(189,plain,
% 182.03/115.73 (m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[188, 78])).
% 182.03/115.73 tff(190,plain,
% 182.03/115.73 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(tautology,[status(thm)],[])).
% 182.03/115.73 tff(191,plain,
% 182.03/115.73 (v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[190, 184])).
% 182.03/115.73 tff(192,plain,
% 182.03/115.73 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, B!1))),
% 182.03/115.73 inference(tautology,[status(thm)],[])).
% 182.03/115.73 tff(193,plain,
% 182.03/115.73 (v1_funct_1(k6_autgroup(A!0, B!1))),
% 182.03/115.73 inference(unit_resolution,[status(thm)],[192, 184])).
% 182.03/115.73 tff(194,plain,
% 182.03/115.73 (^[A: $i, B: $i] : refl((m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 182.03/115.73 inference(bind,[status(th)],[])).
% 182.03/115.73 tff(195,plain,
% 182.03/115.73 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 182.03/115.73 inference(quant_intro,[status(thm)],[194])).
% 182.03/115.73 tff(196,plain,
% 182.03/115.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 182.03/115.73 inference(bind,[status(th)],[])).
% 182.03/115.73 tff(197,plain,
% 182.03/115.73 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 182.03/115.73 inference(quant_intro,[status(thm)],[196])).
% 182.03/115.73 tff(198,plain,
% 182.03/115.73 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 182.03/115.73 inference(rewrite,[status(thm)],[])).
% 182.03/115.73 tff(199,plain,
% 182.03/115.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))))),
% 182.03/115.73 inference(bind,[status(th)],[])).
% 182.03/115.73 tff(200,plain,
% 182.03/115.73 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 182.03/115.73 inference(quant_intro,[status(thm)],[199])).
% 182.03/115.73 tff(201,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_group_1')).
% 182.03/115.73 tff(202,plain,
% 182.03/115.73 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 182.03/115.73 inference(modus_ponens,[status(thm)],[201, 200])).
% 182.03/115.73 tff(203,plain,
% 182.03/115.73 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 182.03/115.73 inference(modus_ponens,[status(thm)],[202, 198])).
% 182.03/115.73 tff(204,plain,(
% 182.03/115.73 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 182.03/115.73 inference(skolemize,[status(sab)],[203])).
% 182.03/115.73 tff(205,plain,
% 182.03/115.73 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 182.03/115.73 inference(modus_ponens,[status(thm)],[204, 197])).
% 182.03/115.73 tff(206,plain,
% 182.03/115.73 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 182.03/115.73 inference(modus_ponens,[status(thm)],[205, 195])).
% 182.03/115.73 tff(207,plain,
% 182.03/115.73 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 182.03/115.73 inference(rewrite,[status(thm)],[])).
% 182.03/115.73 tff(208,plain,
% 182.03/115.73 ((m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 182.03/115.73 inference(rewrite,[status(thm)],[])).
% 182.03/115.73 tff(209,plain,
% 182.03/115.73 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 182.03/115.74 inference(monotonicity,[status(thm)],[208])).
% 182.03/115.74 tff(210,plain,
% 182.03/115.74 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 182.03/115.74 inference(transitivity,[status(thm)],[209, 207])).
% 182.03/115.74 tff(211,plain,
% 182.03/115.74 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(212,plain,
% 182.03/115.74 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[211, 210])).
% 182.03/115.74 tff(213,plain,
% 182.03/115.74 (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[212, 33, 31, 30, 29, 65, 206])).
% 182.03/115.74 tff(214,plain,
% 182.03/115.74 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(215,plain,
% 182.03/115.74 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(216,plain,
% 182.03/115.74 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))))),
% 182.03/115.74 inference(monotonicity,[status(thm)],[215])).
% 182.03/115.74 tff(217,plain,
% 182.03/115.74 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 182.03/115.74 inference(transitivity,[status(thm)],[216, 214])).
% 182.03/115.74 tff(218,plain,
% 182.03/115.74 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(219,plain,
% 182.03/115.74 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[218, 217])).
% 182.03/115.74 tff(220,plain,
% 182.03/115.74 (m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[219, 33, 32, 31, 30, 29, 91, 213])).
% 182.03/115.74 tff(221,plain,
% 182.03/115.74 (((~![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(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, 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(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(222,plain,
% 182.03/115.74 ((~![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(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(223,plain,
% 182.03/115.74 ((~![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(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[222, 221])).
% 182.03/115.74 tff(224,plain,
% 182.03/115.74 (m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[223, 121, 220])).
% 182.03/115.74 tff(225,plain,
% 182.03/115.74 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(226,plain,
% 182.03/115.74 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(227,plain,
% 182.03/115.74 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[226, 225])).
% 182.03/115.74 tff(228,plain,
% 182.03/115.74 (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[227, 180, 224])).
% 182.03/115.74 tff(229,plain,
% 182.03/115.74 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(tautology,[status(thm)],[])).
% 182.03/115.74 tff(230,plain,
% 182.03/115.74 (v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[229, 228])).
% 182.03/115.74 tff(231,plain,
% 182.03/115.74 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 182.03/115.74 inference(tautology,[status(thm)],[])).
% 182.03/115.74 tff(232,plain,
% 182.03/115.74 (v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[231, 228])).
% 182.03/115.74 tff(233,plain,
% 182.03/115.74 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(234,plain,
% 182.03/115.74 (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[233, 76])).
% 182.03/115.74 tff(235,plain,
% 182.03/115.74 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(tautology,[status(thm)],[])).
% 182.03/115.74 tff(236,plain,
% 182.03/115.74 (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[235, 228])).
% 182.03/115.74 tff(237,plain,
% 182.03/115.74 ((~(m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(tautology,[status(thm)],[])).
% 182.03/115.74 tff(238,plain,
% 182.03/115.74 ((~(m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[237, 236])).
% 182.03/115.74 tff(239,plain,
% 182.03/115.74 (m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[238, 234])).
% 182.03/115.74 tff(240,plain,
% 182.03/115.74 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(241,plain,
% 182.03/115.74 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[240])).
% 182.03/115.74 tff(242,plain,
% 182.03/115.74 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(243,plain,
% 182.03/115.74 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(244,plain,
% 182.03/115.74 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[243])).
% 182.03/115.74 tff(245,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 182.03/115.74 tff(246,plain,
% 182.03/115.74 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[245, 244])).
% 182.03/115.74 tff(247,plain,
% 182.03/115.74 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[246, 242])).
% 182.03/115.74 tff(248,plain,(
% 182.03/115.74 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(skolemize,[status(sab)],[247])).
% 182.03/115.74 tff(249,plain,
% 182.03/115.74 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[248, 241])).
% 182.03/115.74 tff(250,plain,
% 182.03/115.74 (((~![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)))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(251,plain,
% 182.03/115.74 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(252,plain,
% 182.03/115.74 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[251, 250])).
% 182.03/115.74 tff(253,plain,
% 182.03/115.74 (l1_struct_0(A!0)),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[252, 29, 249])).
% 182.03/115.74 tff(254,plain,
% 182.03/115.74 (^[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))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(255,plain,
% 182.03/115.74 (![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)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[254])).
% 182.03/115.74 tff(256,plain,
% 182.03/115.74 (^[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)))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(257,plain,
% 182.03/115.74 (![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)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[256])).
% 182.03/115.74 tff(258,plain,
% 182.03/115.74 (![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))))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(259,plain,
% 182.03/115.74 (^[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)))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(260,plain,
% 182.03/115.74 (![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))))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[259])).
% 182.03/115.74 tff(261,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')).
% 182.03/115.74 tff(262,plain,
% 182.03/115.74 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[261, 260])).
% 182.03/115.74 tff(263,plain,
% 182.03/115.74 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[262, 258])).
% 182.03/115.74 tff(264,plain,(
% 182.03/115.74 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 182.03/115.74 inference(skolemize,[status(sab)],[263])).
% 182.03/115.74 tff(265,plain,
% 182.03/115.74 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[264, 257])).
% 182.03/115.74 tff(266,plain,
% 182.03/115.74 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[265, 255])).
% 182.03/115.74 tff(267,plain,
% 182.03/115.74 (((~![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))))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(268,plain,
% 182.03/115.74 ((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))))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(269,plain,
% 182.03/115.74 (((~![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)))))),
% 182.03/115.74 inference(monotonicity,[status(thm)],[268])).
% 182.03/115.74 tff(270,plain,
% 182.03/115.74 (((~![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))))),
% 182.03/115.74 inference(transitivity,[status(thm)],[269, 267])).
% 182.03/115.74 tff(271,plain,
% 182.03/115.74 ((~![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)))),
% 182.03/115.74 inference(quant_inst,[status(thm)],[])).
% 182.03/115.74 tff(272,plain,
% 182.03/115.74 ((~![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)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[271, 270])).
% 182.03/115.74 tff(273,plain,
% 182.03/115.74 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[272, 33, 266])).
% 182.03/115.74 tff(274,plain,
% 182.03/115.74 (~v1_xboole_0(u1_struct_0(A!0))),
% 182.03/115.74 inference(unit_resolution,[status(thm)],[273, 253])).
% 182.03/115.74 tff(275,plain,
% 182.03/115.74 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(276,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[275])).
% 182.03/115.74 tff(277,plain,
% 182.03/115.74 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(278,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[277])).
% 182.03/115.74 tff(279,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 182.03/115.74 inference(rewrite,[status(thm)],[])).
% 182.03/115.74 tff(280,plain,
% 182.03/115.74 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 182.03/115.74 inference(bind,[status(th)],[])).
% 182.03/115.74 tff(281,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 182.03/115.74 inference(quant_intro,[status(thm)],[280])).
% 182.03/115.74 tff(282,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_funct_2')).
% 182.03/115.74 tff(283,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[282, 281])).
% 182.03/115.74 tff(284,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[283, 279])).
% 182.03/115.74 tff(285,plain,(
% 182.03/115.74 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 182.03/115.74 inference(skolemize,[status(sab)],[284])).
% 182.03/115.74 tff(286,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[285, 278])).
% 182.03/115.74 tff(287,plain,
% 182.03/115.74 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 182.03/115.74 inference(modus_ponens,[status(thm)],[286, 276])).
% 182.03/115.74 tff(288,plain,
% 182.03/115.74 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(289,plain,
% 182.03/115.75 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(290,plain,
% 182.03/115.75 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))))),
% 182.03/115.75 inference(monotonicity,[status(thm)],[289])).
% 182.03/115.75 tff(291,plain,
% 182.03/115.75 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 182.03/115.75 inference(transitivity,[status(thm)],[290, 288])).
% 182.03/115.75 tff(292,plain,
% 182.03/115.75 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 182.03/115.75 inference(quant_inst,[status(thm)],[])).
% 182.03/115.75 tff(293,plain,
% 182.03/115.75 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[292, 291])).
% 182.03/115.75 tff(294,plain,
% 182.03/115.75 ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))),
% 182.03/115.75 inference(unit_resolution,[status(thm)],[293, 287, 274])).
% 182.03/115.75 tff(295,plain,
% 182.03/115.75 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 182.03/115.75 inference(unit_resolution,[status(thm)],[294, 239, 232, 230, 193, 191, 189])).
% 182.03/115.75 tff(296,plain,
% 182.03/115.75 (k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 182.03/115.75 inference(symmetry,[status(thm)],[295])).
% 182.03/115.75 tff(297,plain,
% 182.03/115.75 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl(((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(298,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[297])).
% 182.03/115.75 tff(299,plain,
% 182.03/115.75 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)) <=> (~((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) <=> (~(~((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))))), rewrite((~(~((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))) <=> ((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) <=> ((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), (((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> (((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite((((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), (((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(300,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[299])).
% 182.03/115.75 tff(301,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(302,plain,
% 182.03/115.75 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) <=> (v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F))), ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) <=> ((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F)) & m1_relset_1(F, C, D)))), rewrite(((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F)) & m1_relset_1(F, C, D)) <=> (v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))), ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) <=> (v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)))), (((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite(((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))), (((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(303,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[302])).
% 182.03/115.75 tff(304,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_partfun1')).
% 182.03/115.75 tff(305,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[304, 303])).
% 182.03/115.75 tff(306,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[305, 301])).
% 182.03/115.75 tff(307,plain,(
% 182.03/115.75 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 182.03/115.75 inference(skolemize,[status(sab)],[306])).
% 182.03/115.75 tff(308,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[307, 300])).
% 182.03/115.75 tff(309,plain,
% 182.03/115.75 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[308, 298])).
% 182.03/115.75 tff(310,plain,
% 182.03/115.75 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(311,plain,
% 182.03/115.75 (((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(312,plain,
% 182.03/115.75 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))))),
% 182.03/115.75 inference(monotonicity,[status(thm)],[311])).
% 182.03/115.75 tff(313,plain,
% 182.03/115.75 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 182.03/115.75 inference(transitivity,[status(thm)],[312, 310])).
% 182.03/115.75 tff(314,plain,
% 182.03/115.75 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 182.03/115.75 inference(quant_inst,[status(thm)],[])).
% 182.03/115.75 tff(315,plain,
% 182.03/115.75 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[314, 313])).
% 182.03/115.75 tff(316,plain,
% 182.03/115.75 (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 182.03/115.75 inference(unit_resolution,[status(thm)],[315, 309, 193, 232, 239, 189])).
% 182.03/115.75 tff(317,plain,
% 182.03/115.75 (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))),
% 182.03/115.75 inference(transitivity,[status(thm)],[316, 296, 69, 40])).
% 182.03/115.75 tff(318,assumption,(~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))), introduced(assumption)).
% 182.03/115.75 tff(319,plain,
% 182.03/115.75 ($false),
% 182.03/115.75 inference(unit_resolution,[status(thm)],[318, 317])).
% 182.03/115.75 tff(320,plain,(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))), inference(lemma,lemma(discharge,[]))).
% 182.03/115.75 tff(321,plain,
% 182.03/115.75 (^[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] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(322,plain,
% 182.03/115.75 (![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[321])).
% 182.03/115.75 tff(323,plain,
% 182.03/115.75 (^[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] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(324,plain,
% 182.03/115.75 (![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[323])).
% 182.03/115.75 tff(325,plain,
% 182.03/115.75 (![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(transitivity,[status(thm)],[324, 322])).
% 182.03/115.75 tff(326,plain,
% 182.03/115.75 (^[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] : rewrite(((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))), (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(327,plain,
% 182.03/115.75 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[326])).
% 182.03/115.75 tff(328,plain,
% 182.03/115.75 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(329,plain,
% 182.03/115.75 (^[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), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = 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)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(bind,[status(th)],[])).
% 182.03/115.75 tff(330,plain,
% 182.03/115.75 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 182.03/115.75 inference(quant_intro,[status(thm)],[329])).
% 182.03/115.75 tff(331,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l9_autgroup')).
% 182.03/115.75 tff(332,plain,
% 182.03/115.75 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[331, 330])).
% 182.03/115.75 tff(333,plain,
% 182.03/115.75 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[332, 328])).
% 182.03/115.75 tff(334,plain,(
% 182.03/115.75 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 182.03/115.75 inference(skolemize,[status(sab)],[333])).
% 182.03/115.75 tff(335,plain,
% 182.03/115.75 (![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[334, 327])).
% 182.03/115.75 tff(336,plain,
% 182.03/115.75 (![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[335, 325])).
% 182.03/115.75 tff(337,plain,
% 182.03/115.75 (((~![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(338,plain,
% 182.03/115.75 ((~![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))),
% 182.03/115.75 inference(quant_inst,[status(thm)],[])).
% 182.03/115.75 tff(339,plain,
% 182.03/115.75 ((~![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), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(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), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))),
% 182.03/115.75 inference(modus_ponens,[status(thm)],[338, 337])).
% 182.03/115.75 tff(340,plain,
% 182.03/115.75 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))),
% 182.03/115.75 inference(unit_resolution,[status(thm)],[339, 33, 32, 31, 30, 29, 336])).
% 182.03/115.75 tff(341,plain,
% 182.03/115.75 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))))),
% 182.03/115.75 inference(rewrite,[status(thm)],[])).
% 182.03/115.75 tff(342,plain,
% 182.03/115.75 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))))),
% 182.03/115.76 inference(quant_inst,[status(thm)],[])).
% 182.03/115.76 tff(343,plain,
% 182.03/115.76 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)))))),
% 182.03/115.76 inference(modus_ponens,[status(thm)],[342, 341])).
% 182.03/115.76 tff(344,plain,
% 182.03/115.76 (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))),
% 182.03/115.76 inference(unit_resolution,[status(thm)],[343, 340, 125])).
% 182.03/115.76 tff(345,plain,
% 182.03/115.76 (((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)))) | (k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))),
% 182.03/115.76 inference(tautology,[status(thm)],[])).
% 182.03/115.76 tff(346,plain,
% 182.03/115.76 (k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)),
% 182.03/115.76 inference(unit_resolution,[status(thm)],[345, 344])).
% 182.03/115.76 tff(347,plain,
% 182.03/115.76 (((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)))) | (k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))),
% 182.03/115.76 inference(tautology,[status(thm)],[])).
% 182.03/115.76 tff(348,plain,
% 182.03/115.76 (k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1))),
% 182.03/115.76 inference(unit_resolution,[status(thm)],[347, 344])).
% 182.03/115.76 tff(349,plain,
% 182.03/115.76 (k2_relat_1(k6_autgroup(A!0, B!1)) = k1_relat_1(k6_autgroup(A!0, B!1))),
% 182.03/115.76 inference(symmetry,[status(thm)],[348])).
% 182.03/115.76 tff(350,plain,
% 182.03/115.76 (k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)),
% 182.03/115.76 inference(transitivity,[status(thm)],[349, 346])).
% 182.03/115.76 tff(351,plain,
% 182.03/115.76 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(bind,[status(th)],[])).
% 182.03/115.76 tff(352,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 182.03/115.76 inference(quant_intro,[status(thm)],[351])).
% 182.03/115.76 tff(353,plain,
% 182.03/115.76 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(bind,[status(th)],[])).
% 182.03/115.76 tff(354,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 182.03/115.76 inference(quant_intro,[status(thm)],[353])).
% 182.03/115.76 tff(355,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 182.03/115.76 inference(transitivity,[status(thm)],[354, 352])).
% 182.03/115.76 tff(356,plain,
% 182.03/115.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) <=> (~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> (~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))))), rewrite((~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)) <=> (~((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))), ((~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) <=> (~(~((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))))), rewrite((~(~((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))) <=> ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)))), ((~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) <=> ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))), trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), ((~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))), ((~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), (((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))) | ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))), rewrite(((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))) | ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))), (((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))), (![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))) <=> ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> (((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))), rewrite((((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))))),
% 182.03/115.76 inference(bind,[status(th)],[])).
% 182.03/115.76 tff(357,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 182.03/115.76 inference(quant_intro,[status(thm)],[356])).
% 182.03/115.76 tff(358,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(rewrite,[status(thm)],[])).
% 182.03/115.76 tff(359,plain,
% 182.03/115.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) <=> (v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))), trans(monotonicity(rewrite((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) <=> ((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))), trans(monotonicity(rewrite(((A = k1_xboole_0) | (B = k1_xboole_0)) <=> ((B = k1_xboole_0) | (A = k1_xboole_0))), ((((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))) <=> (((B = k1_xboole_0) | (A = k1_xboole_0)) | (D = k2_funct_1(C))))), rewrite((((B = k1_xboole_0) | (A = k1_xboole_0)) | (D = k2_funct_1(C))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)))), ((((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C))))), (((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))) <=> (((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)))))), rewrite((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))))), (((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)))))), ((((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))) <=> ((v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))), ((((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))) <=> ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))))),
% 182.03/115.76 inference(bind,[status(th)],[])).
% 182.03/115.76 tff(360,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(quant_intro,[status(thm)],[359])).
% 182.03/115.76 tff(361,axiom,(![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_funct_2')).
% 182.03/115.76 tff(362,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(modus_ponens,[status(thm)],[361, 360])).
% 182.03/115.76 tff(363,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(modus_ponens,[status(thm)],[362, 358])).
% 182.03/115.76 tff(364,plain,(
% 182.03/115.76 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 182.03/115.76 inference(skolemize,[status(sab)],[363])).
% 182.03/115.76 tff(365,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 182.03/115.76 inference(modus_ponens,[status(thm)],[364, 357])).
% 182.03/115.76 tff(366,plain,
% 182.03/115.76 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 182.03/115.76 inference(modus_ponens,[status(thm)],[365, 355])).
% 182.03/115.76 tff(367,plain,
% 182.03/115.76 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.76 inference(rewrite,[status(thm)],[])).
% 182.03/115.76 tff(368,plain,
% 182.03/115.76 (((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.76 inference(rewrite,[status(thm)],[])).
% 182.03/115.76 tff(369,plain,
% 182.03/115.76 (^[D: $i] : rewrite(((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.76 inference(bind,[status(th)],[])).
% 182.03/115.76 tff(370,plain,
% 182.03/115.76 (![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.76 inference(quant_intro,[status(thm)],[369])).
% 182.03/115.76 tff(371,plain,
% 182.03/115.76 (((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.76 inference(monotonicity,[status(thm)],[370])).
% 182.03/115.76 tff(372,plain,
% 182.03/115.76 (((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.76 inference(transitivity,[status(thm)],[371, 368])).
% 182.03/115.76 tff(373,plain,
% 182.03/115.76 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))))),
% 182.03/115.76 inference(monotonicity,[status(thm)],[372])).
% 182.03/115.76 tff(374,plain,
% 182.03/115.76 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.76 inference(transitivity,[status(thm)],[373, 367])).
% 182.03/115.76 tff(375,plain,
% 182.03/115.76 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 182.03/115.76 inference(quant_inst,[status(thm)],[])).
% 182.03/115.76 tff(376,plain,
% 182.03/115.76 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[375, 374])).
% 182.03/115.77 tff(377,plain,
% 182.03/115.77 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[376, 366, 193, 191, 186])).
% 182.03/115.77 tff(378,plain,
% 182.03/115.77 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)),
% 182.03/115.77 inference(tautology,[status(thm)],[])).
% 182.03/115.77 tff(379,plain,
% 182.03/115.77 (v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[378, 184])).
% 182.03/115.77 tff(380,plain,
% 182.03/115.77 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))),
% 182.03/115.77 inference(tautology,[status(thm)],[])).
% 182.03/115.77 tff(381,plain,
% 182.03/115.77 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[380, 178])).
% 182.03/115.77 tff(382,plain,
% 182.03/115.77 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(383,plain,
% 182.03/115.77 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))))),
% 182.03/115.77 inference(quant_inst,[status(thm)],[])).
% 182.03/115.77 tff(384,plain,
% 182.03/115.77 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0)))))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[383, 382])).
% 182.03/115.77 tff(385,plain,
% 182.03/115.77 (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[384, 193, 381, 191, 379, 186])).
% 182.03/115.77 tff(386,plain,
% 182.03/115.77 (^[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))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(387,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[386])).
% 182.03/115.77 tff(388,plain,
% 182.03/115.77 (^[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))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(389,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[388])).
% 182.03/115.77 tff(390,plain,
% 182.03/115.77 (^[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))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(391,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[390])).
% 182.03/115.77 tff(392,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(transitivity,[status(thm)],[391, 389])).
% 182.03/115.77 tff(393,plain,
% 182.03/115.77 (^[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)))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(394,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[393])).
% 182.03/115.77 tff(395,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(396,plain,
% 182.03/115.77 (^[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))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(397,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[396])).
% 182.03/115.77 tff(398,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')).
% 182.03/115.77 tff(399,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[398, 397])).
% 182.03/115.77 tff(400,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[399, 395])).
% 182.03/115.77 tff(401,plain,(
% 182.03/115.77 ![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)))),
% 182.03/115.77 inference(skolemize,[status(sab)],[400])).
% 182.03/115.77 tff(402,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[401, 394])).
% 182.03/115.77 tff(403,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[402, 392])).
% 182.03/115.77 tff(404,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[403, 387])).
% 182.03/115.77 tff(405,plain,
% 182.03/115.77 (((~![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))))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(406,plain,
% 182.03/115.77 ((~![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))))),
% 182.03/115.77 inference(quant_inst,[status(thm)],[])).
% 182.03/115.77 tff(407,plain,
% 182.03/115.77 ((~![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)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[406, 405])).
% 182.03/115.77 tff(408,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[407, 404, 274, 171])).
% 182.03/115.77 tff(409,plain,
% 182.03/115.77 ((~![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(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 182.03/115.77 inference(quant_inst,[status(thm)],[])).
% 182.03/115.77 tff(410,plain,
% 182.03/115.77 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[409, 408])).
% 182.03/115.77 tff(411,plain,
% 182.03/115.77 ((~(m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 182.03/115.77 inference(tautology,[status(thm)],[])).
% 182.03/115.77 tff(412,plain,
% 182.03/115.77 ((~(m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) | m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[411, 125])).
% 182.03/115.77 tff(413,plain,
% 182.03/115.77 (m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[412, 410])).
% 182.03/115.77 tff(414,plain,
% 182.03/115.77 (^[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))))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(415,plain,
% 182.03/115.77 (![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)))))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[414])).
% 182.03/115.77 tff(416,plain,
% 182.03/115.77 (^[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))))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(417,plain,
% 182.03/115.77 (![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)))))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[416])).
% 182.03/115.77 tff(418,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(419,plain,
% 182.03/115.77 (^[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))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(420,plain,
% 182.03/115.77 (![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)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[419])).
% 182.03/115.77 tff(421,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')).
% 182.03/115.77 tff(422,plain,
% 182.03/115.77 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[421, 420])).
% 182.03/115.77 tff(423,plain,
% 182.03/115.77 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[422, 418])).
% 182.03/115.77 tff(424,plain,(
% 182.03/115.77 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 182.03/115.77 inference(skolemize,[status(sab)],[423])).
% 182.03/115.77 tff(425,plain,
% 182.03/115.77 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[424, 417])).
% 182.03/115.77 tff(426,plain,
% 182.03/115.77 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[425, 415])).
% 182.03/115.77 tff(427,plain,
% 182.03/115.77 (((~![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))))))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(428,plain,
% 182.03/115.77 ((~![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))))))),
% 182.03/115.77 inference(quant_inst,[status(thm)],[])).
% 182.03/115.77 tff(429,plain,
% 182.03/115.77 ((~![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)))))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[428, 427])).
% 182.03/115.77 tff(430,plain,
% 182.03/115.77 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[429, 426, 171])).
% 182.03/115.77 tff(431,plain,
% 182.03/115.77 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 182.03/115.77 inference(tautology,[status(thm)],[])).
% 182.03/115.77 tff(432,plain,
% 182.03/115.77 (~v1_xboole_0(k1_autgroup(A!0))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[431, 430])).
% 182.03/115.77 tff(433,plain,
% 182.03/115.77 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(434,plain,
% 182.03/115.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[433])).
% 182.03/115.77 tff(435,plain,
% 182.03/115.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(436,plain,
% 182.03/115.77 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 182.03/115.77 inference(bind,[status(th)],[])).
% 182.03/115.77 tff(437,plain,
% 182.03/115.77 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(quant_intro,[status(thm)],[436])).
% 182.03/115.77 tff(438,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 182.03/115.77 tff(439,plain,
% 182.03/115.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[438, 437])).
% 182.03/115.77 tff(440,plain,
% 182.03/115.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[439, 435])).
% 182.03/115.77 tff(441,plain,(
% 182.03/115.77 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(skolemize,[status(sab)],[440])).
% 182.03/115.77 tff(442,plain,
% 182.03/115.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[441, 434])).
% 182.03/115.77 tff(443,plain,
% 182.03/115.77 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(444,plain,
% 182.03/115.77 ((r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) <=> (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(445,plain,
% 182.03/115.77 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))),
% 182.03/115.77 inference(monotonicity,[status(thm)],[444])).
% 182.03/115.77 tff(446,plain,
% 182.03/115.77 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 182.03/115.77 inference(transitivity,[status(thm)],[445, 443])).
% 182.03/115.77 tff(447,plain,
% 182.03/115.77 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))),
% 182.03/115.77 inference(quant_inst,[status(thm)],[])).
% 182.03/115.77 tff(448,plain,
% 182.03/115.77 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 182.03/115.77 inference(modus_ponens,[status(thm)],[447, 446])).
% 182.03/115.77 tff(449,plain,
% 182.03/115.77 (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[448, 442, 432, 413])).
% 182.03/115.77 tff(450,plain,
% 182.03/115.77 ((~(r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0)))))) | (~r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))),
% 182.03/115.77 inference(tautology,[status(thm)],[])).
% 182.03/115.77 tff(451,plain,
% 182.03/115.77 ((~(r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) <=> (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0)))))) | (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[450, 449])).
% 182.03/115.77 tff(452,plain,
% 182.03/115.77 (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0)))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[451, 385])).
% 182.03/115.77 tff(453,plain,
% 182.03/115.77 (((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) | v2_funct_1(k6_autgroup(A!0, B!1))),
% 182.03/115.77 inference(tautology,[status(thm)],[])).
% 182.03/115.77 tff(454,plain,
% 182.03/115.77 (v2_funct_1(k6_autgroup(A!0, B!1))),
% 182.03/115.77 inference(unit_resolution,[status(thm)],[453, 452])).
% 182.03/115.77 tff(455,plain,
% 182.03/115.77 (~(k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1)))),
% 182.03/115.77 inference(or_elim,[status(thm)],[64])).
% 182.03/115.77 tff(456,plain,
% 182.03/115.77 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.77 inference(rewrite,[status(thm)],[])).
% 182.03/115.77 tff(457,plain,
% 182.03/115.77 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))) <=> ((k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.78 inference(rewrite,[status(thm)],[])).
% 182.03/115.78 tff(458,plain,
% 182.03/115.78 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))))),
% 182.03/115.78 inference(monotonicity,[status(thm)],[457])).
% 182.03/115.78 tff(459,plain,
% 182.03/115.78 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.78 inference(transitivity,[status(thm)],[458, 456])).
% 182.03/115.78 tff(460,plain,
% 182.03/115.78 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 182.03/115.78 inference(quant_inst,[status(thm)],[])).
% 182.03/115.78 tff(461,plain,
% 182.03/115.78 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))),
% 182.03/115.78 inference(modus_ponens,[status(thm)],[460, 459])).
% 182.03/115.78 tff(462,plain,
% 182.03/115.78 ((u1_struct_0(A!0) = k1_xboole_0) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))),
% 182.03/115.78 inference(unit_resolution,[status(thm)],[461, 455, 232, 230, 236, 454, 377, 350])).
% 182.03/115.78 tff(463,plain,
% 182.03/115.78 (u1_struct_0(A!0) = k1_xboole_0),
% 182.03/115.78 inference(unit_resolution,[status(thm)],[462, 320])).
% 182.03/115.78 tff(464,plain,
% 182.03/115.78 (v1_xboole_0(u1_struct_0(A!0)) <=> v1_xboole_0(k1_xboole_0)),
% 182.03/115.78 inference(monotonicity,[status(thm)],[463])).
% 182.03/115.78 tff(465,plain,
% 182.03/115.78 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(u1_struct_0(A!0))),
% 182.03/115.78 inference(symmetry,[status(thm)],[464])).
% 182.03/115.78 tff(466,plain,
% 182.03/115.78 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 182.03/115.78 inference(rewrite,[status(thm)],[])).
% 182.03/115.78 tff(467,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 182.03/115.78 tff(468,plain,
% 182.03/115.78 (v1_xboole_0(k1_xboole_0)),
% 182.03/115.78 inference(modus_ponens,[status(thm)],[467, 466])).
% 182.03/115.78 tff(469,plain,
% 182.03/115.78 (v1_xboole_0(u1_struct_0(A!0))),
% 182.13/115.81 inference(modus_ponens,[status(thm)],[468, 465])).
% 182.13/115.81 tff(470,plain,
% 182.13/115.81 ($false),
% 182.13/115.81 inference(unit_resolution,[status(thm)],[274, 469])).
% 182.13/115.81 % SZS output end Proof
%------------------------------------------------------------------------------