TSTP Solution File: GRP631+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP631+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 0.98s 0.86s
% Output : Proof 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP631+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 18:27:27 EDT 2022
% 0.13/0.34 % 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.
% 0.98/0.86 % SZS status Theorem
% 0.98/0.86 % SZS output start Proof
% 0.98/0.86 tff(k6_autgroup_type, type, (
% 0.98/0.86 k6_autgroup: ( $i * $i ) > $i)).
% 0.98/0.86 tff(tptp_fun_B_1_type, type, (
% 0.98/0.86 tptp_fun_B_1: $i)).
% 0.98/0.86 tff(tptp_fun_A_0_type, type, (
% 0.98/0.86 tptp_fun_A_0: $i)).
% 0.98/0.86 tff(k7_funct_2_type, type, (
% 0.98/0.86 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.98/0.86 tff(k2_group_1_type, type, (
% 0.98/0.86 k2_group_1: $i > $i)).
% 0.98/0.86 tff(u1_struct_0_type, type, (
% 0.98/0.86 u1_struct_0: $i > $i)).
% 0.98/0.86 tff(k7_relset_1_type, type, (
% 0.98/0.86 k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.98/0.86 tff(k6_partfun1_type, type, (
% 0.98/0.86 k6_partfun1: $i > $i)).
% 0.98/0.86 tff(m2_relset_1_type, type, (
% 0.98/0.86 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.98/0.86 tff(v1_funct_2_type, type, (
% 0.98/0.86 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.98/0.86 tff(v1_funct_1_type, type, (
% 0.98/0.86 v1_funct_1: $i > $o)).
% 0.98/0.86 tff(m2_fraenkel_type, type, (
% 0.98/0.86 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.98/0.86 tff(k4_autgroup_type, type, (
% 0.98/0.86 k4_autgroup: $i > $i)).
% 0.98/0.86 tff(m1_fraenkel_type, type, (
% 0.98/0.86 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.98/0.86 tff(v4_group_1_type, type, (
% 0.98/0.86 v4_group_1: $i > $o)).
% 0.98/0.86 tff(v3_group_1_type, type, (
% 0.98/0.86 v3_group_1: $i > $o)).
% 0.98/0.86 tff(l1_group_1_type, type, (
% 0.98/0.86 l1_group_1: $i > $o)).
% 0.98/0.86 tff(v1_group_1_type, type, (
% 0.98/0.86 v1_group_1: $i > $o)).
% 0.98/0.86 tff(v3_struct_0_type, type, (
% 0.98/0.86 v3_struct_0: $i > $o)).
% 0.98/0.86 tff(m1_subset_1_type, type, (
% 0.98/0.86 m1_subset_1: ( $i * $i ) > $o)).
% 0.98/0.86 tff(v1_xboole_0_type, type, (
% 0.98/0.86 v1_xboole_0: $i > $o)).
% 0.98/0.86 tff(l1_struct_0_type, type, (
% 0.98/0.86 l1_struct_0: $i > $o)).
% 0.98/0.86 tff(k5_relat_1_type, type, (
% 0.98/0.86 k5_relat_1: ( $i * $i ) > $i)).
% 0.98/0.86 tff(m1_relset_1_type, type, (
% 0.98/0.86 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.98/0.86 tff(v1_partfun1_type, type, (
% 0.98/0.86 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.98/0.86 tff(g1_group_1_type, type, (
% 0.98/0.86 g1_group_1: ( $i * $i ) > $i)).
% 0.98/0.86 tff(u1_group_1_type, type, (
% 0.98/0.86 u1_group_1: $i > $i)).
% 0.98/0.86 tff(k6_relat_1_type, type, (
% 0.98/0.86 k6_relat_1: $i > $i)).
% 0.98/0.86 tff(v8_relat_2_type, type, (
% 0.98/0.86 v8_relat_2: $i > $o)).
% 0.98/0.86 tff(v4_relat_2_type, type, (
% 0.98/0.86 v4_relat_2: $i > $o)).
% 0.98/0.86 tff(v3_relat_2_type, type, (
% 0.98/0.86 v3_relat_2: $i > $o)).
% 0.98/0.86 tff(v1_relat_2_type, type, (
% 0.98/0.86 v1_relat_2: $i > $o)).
% 0.98/0.86 tff(v1_relat_1_type, type, (
% 0.98/0.86 v1_relat_1: $i > $o)).
% 0.98/0.86 tff(1,plain,
% 0.98/0.86 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k4_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(k4_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))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(2,plain,
% 0.98/0.86 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[1])).
% 0.98/0.86 tff(3,plain,
% 0.98/0.86 (^[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(k4_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(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_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)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(4,plain,
% 0.98/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[3])).
% 0.98/0.86 tff(5,plain,
% 0.98/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(6,plain,
% 0.98/0.86 (^[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(k4_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(k4_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(k4_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(k4_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(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(7,plain,
% 0.98/0.86 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[6])).
% 0.98/0.86 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)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 0.98/0.86 tff(9,plain,
% 0.98/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.98/0.86 tff(10,plain,
% 0.98/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.98/0.86 tff(11,plain,(
% 0.98/0.86 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.98/0.86 inference(skolemize,[status(sab)],[10])).
% 0.98/0.86 tff(12,plain,
% 0.98/0.86 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.98/0.86 tff(13,plain,
% 0.98/0.86 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.98/0.86 tff(14,plain,
% 0.98/0.86 ((((~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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = 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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(15,plain,
% 0.98/0.86 ((~(~((~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))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(16,plain,
% 0.98/0.86 (((~(~((~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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = 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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[15])).
% 0.98/0.86 tff(17,plain,
% 0.98/0.86 (((~(~((~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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = 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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))))),
% 0.98/0.86 inference(transitivity,[status(thm)],[16, 14])).
% 0.98/0.86 tff(18,plain,
% 0.98/0.86 ((~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = 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))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B))))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(19,plain,
% 0.98/0.86 ((~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = 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))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B))))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 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)) => ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t29_autgroup')).
% 0.98/0.86 tff(21,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.98/0.86 tff(22,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.98/0.86 tff(23,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.98/0.86 tff(24,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.98/0.86 tff(25,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.98/0.86 tff(26,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.98/0.86 tff(27,plain,
% 0.98/0.86 (~![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, k2_group_1(A)), k6_autgroup(A, B)) = k6_autgroup(A, B)) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k2_group_1(A))) = k6_autgroup(A, B)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.98/0.86 tff(28,plain,
% 0.98/0.86 ((~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))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1)))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.98/0.86 tff(29,plain,
% 0.98/0.86 (l1_group_1(A!0)),
% 0.98/0.86 inference(and_elim,[status(thm)],[28])).
% 0.98/0.86 tff(30,plain,
% 0.98/0.86 (v4_group_1(A!0)),
% 0.98/0.86 inference(and_elim,[status(thm)],[28])).
% 0.98/0.86 tff(31,plain,
% 0.98/0.86 (v3_group_1(A!0)),
% 0.98/0.86 inference(and_elim,[status(thm)],[28])).
% 0.98/0.86 tff(32,plain,
% 0.98/0.86 (v1_group_1(A!0)),
% 0.98/0.86 inference(and_elim,[status(thm)],[28])).
% 0.98/0.86 tff(33,plain,
% 0.98/0.86 (~v3_struct_0(A!0)),
% 0.98/0.86 inference(and_elim,[status(thm)],[28])).
% 0.98/0.86 tff(34,plain,
% 0.98/0.86 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(35,plain,
% 0.98/0.86 ((v3_struct_0(A!0) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(36,plain,
% 0.98/0.86 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[35])).
% 0.98/0.86 tff(37,plain,
% 0.98/0.86 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.98/0.86 inference(transitivity,[status(thm)],[36, 34])).
% 0.98/0.86 tff(38,plain,
% 0.98/0.86 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(39,plain,
% 0.98/0.86 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.98/0.86 tff(40,plain,
% 0.98/0.86 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[39, 33, 32, 31, 30, 29, 13])).
% 0.98/0.86 tff(41,plain,
% 0.98/0.86 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(42,plain,
% 0.98/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[41])).
% 0.98/0.86 tff(43,plain,
% 0.98/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(44,plain,
% 0.98/0.86 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(45,plain,
% 0.98/0.86 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[44])).
% 0.98/0.86 tff(46,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.98/0.86 tff(47,plain,
% 0.98/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.98/0.86 tff(48,plain,
% 0.98/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.98/0.86 tff(49,plain,(
% 0.98/0.86 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(skolemize,[status(sab)],[48])).
% 0.98/0.86 tff(50,plain,
% 0.98/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.98/0.86 tff(51,plain,
% 0.98/0.86 (((~![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)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(52,plain,
% 0.98/0.86 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(53,plain,
% 0.98/0.86 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.98/0.86 tff(54,plain,
% 0.98/0.86 (l1_struct_0(A!0)),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[53, 29, 50])).
% 0.98/0.86 tff(55,plain,
% 0.98/0.86 (^[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))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(56,plain,
% 0.98/0.86 (![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)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[55])).
% 0.98/0.86 tff(57,plain,
% 0.98/0.86 (^[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)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(58,plain,
% 0.98/0.86 (![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)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[57])).
% 0.98/0.86 tff(59,plain,
% 0.98/0.86 (![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))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(60,plain,
% 0.98/0.86 (^[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)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(61,plain,
% 0.98/0.86 (![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))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[60])).
% 0.98/0.86 tff(62,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')).
% 0.98/0.86 tff(63,plain,
% 0.98/0.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.98/0.87 tff(64,plain,
% 0.98/0.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.98/0.87 tff(65,plain,(
% 0.98/0.87 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.98/0.87 inference(skolemize,[status(sab)],[64])).
% 0.98/0.87 tff(66,plain,
% 0.98/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.98/0.87 tff(67,plain,
% 0.98/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.98/0.87 tff(68,plain,
% 0.98/0.87 (((~![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))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(69,plain,
% 0.98/0.87 ((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))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(70,plain,
% 0.98/0.87 (((~![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)))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[69])).
% 0.98/0.87 tff(71,plain,
% 0.98/0.87 (((~![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))))),
% 0.98/0.87 inference(transitivity,[status(thm)],[70, 68])).
% 0.98/0.87 tff(72,plain,
% 0.98/0.87 ((~![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)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(73,plain,
% 0.98/0.87 ((~![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)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.98/0.87 tff(74,plain,
% 0.98/0.87 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[73, 33, 67])).
% 0.98/0.87 tff(75,plain,
% 0.98/0.87 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[74, 54])).
% 0.98/0.87 tff(76,plain,
% 0.98/0.87 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(77,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[76])).
% 0.98/0.87 tff(78,plain,
% 0.98/0.87 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(79,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[78])).
% 0.98/0.87 tff(80,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(transitivity,[status(thm)],[79, 77])).
% 0.98/0.87 tff(81,plain,
% 0.98/0.87 (^[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))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(82,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[81])).
% 0.98/0.87 tff(83,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, 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)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(84,plain,
% 0.98/0.87 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> (m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), rewrite((m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), (![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(85,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, 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)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[84])).
% 0.98/0.87 tff(86,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_fraenkel')).
% 0.98/0.87 tff(87,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.98/0.87 tff(88,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.98/0.87 tff(89,plain,(
% 0.98/0.87 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.98/0.87 inference(skolemize,[status(sab)],[88])).
% 0.98/0.87 tff(90,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.98/0.87 tff(91,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.98/0.87 tff(92,plain,
% 0.98/0.87 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(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)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(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)))))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(93,plain,
% 0.98/0.87 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(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)))))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(94,plain,
% 0.98/0.87 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(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))))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.98/0.87 tff(95,plain,
% 0.98/0.87 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[94, 91, 75, 40])).
% 0.98/0.87 tff(96,plain,
% 0.98/0.87 (^[A: $i, B: $i] : refl((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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(97,plain,
% 0.98/0.87 (![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[96])).
% 0.98/0.87 tff(98,plain,
% 0.98/0.87 (^[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))) | (~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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v1_group_1(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))) | (~v1_group_1(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))) | (~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) | (~m1_subset_1(B, u1_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)))) | 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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(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))) | (~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)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(99,plain,
% 0.98/0.87 (![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] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[98])).
% 0.98/0.87 tff(100,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(101,plain,
% 0.98/0.87 (^[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)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(102,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[101])).
% 0.98/0.87 tff(103,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')).
% 0.98/0.87 tff(104,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.98/0.87 tff(105,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.98/0.87 tff(106,plain,(
% 0.98/0.87 ![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)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[105])).
% 0.98/0.87 tff(107,plain,
% 0.98/0.87 (![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.98/0.87 tff(108,plain,
% 0.98/0.87 (![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.98/0.87 tff(109,plain,
% 0.98/0.87 (~((~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, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))),
% 0.98/0.87 inference(and_elim,[status(thm)],[28])).
% 0.98/0.87 tff(110,plain,
% 0.98/0.87 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.98/0.87 inference(or_elim,[status(thm)],[109])).
% 0.98/0.87 tff(111,plain,
% 0.98/0.87 (((~![A: $i, B: $i] : (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))) | (~v1_group_1(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) | (~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] : (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))) | (~v1_group_1(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) | (~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)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(112,plain,
% 0.98/0.87 ((m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_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))) | 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)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(113,plain,
% 0.98/0.87 (((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (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))) | (~v1_group_1(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) | (~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))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[112])).
% 0.98/0.87 tff(114,plain,
% 0.98/0.87 (((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (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))) | (~v1_group_1(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) | (~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)))),
% 0.98/0.87 inference(transitivity,[status(thm)],[113, 111])).
% 0.98/0.87 tff(115,plain,
% 0.98/0.87 ((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(116,plain,
% 0.98/0.87 ((~![A: $i, B: $i] : (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))) | (~v1_group_1(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) | (~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))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.98/0.87 tff(117,plain,
% 0.98/0.87 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[116, 33, 32, 31, 30, 29, 110, 108])).
% 0.98/0.87 tff(118,plain,
% 0.98/0.87 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_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))) | (~m2_relset_1(k6_autgroup(A!0, B!1), 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), k4_autgroup(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))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_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))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(119,plain,
% 0.98/0.87 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_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))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(120,plain,
% 0.98/0.87 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_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))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.98/0.87 tff(121,plain,
% 0.98/0.87 (~((~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))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[120, 117, 95])).
% 0.98/0.87 tff(122,plain,
% 0.98/0.87 (((~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)))) | m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.87 inference(tautology,[status(thm)],[])).
% 0.98/0.87 tff(123,plain,
% 0.98/0.87 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.98/0.87 tff(124,plain,
% 0.98/0.87 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(125,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[124])).
% 0.98/0.87 tff(126,plain,
% 0.98/0.87 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(127,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[126])).
% 0.98/0.87 tff(128,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(129,plain,
% 0.98/0.87 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(130,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[129])).
% 0.98/0.87 tff(131,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_2')).
% 0.98/0.87 tff(132,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.98/0.87 tff(133,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.98/0.87 tff(134,plain,(
% 0.98/0.87 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[133])).
% 0.98/0.87 tff(135,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.98/0.87 tff(136,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.98/0.87 tff(137,plain,
% 0.98/0.87 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1))))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(138,plain,
% 0.98/0.87 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1))))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(139,plain,
% 0.98/0.87 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1)))))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.98/0.87 tff(140,plain,
% 0.98/0.87 (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1))))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[139, 136, 123])).
% 0.98/0.87 tff(141,plain,
% 0.98/0.87 (((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1)))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))),
% 0.98/0.87 inference(tautology,[status(thm)],[])).
% 0.98/0.87 tff(142,plain,
% 0.98/0.87 (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.98/0.87 tff(143,plain,
% 0.98/0.87 (^[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)))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(144,plain,
% 0.98/0.87 (![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))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[143])).
% 0.98/0.87 tff(145,plain,
% 0.98/0.87 (![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))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(146,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')).
% 0.98/0.87 tff(147,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.98/0.87 tff(148,plain,(
% 0.98/0.87 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.98/0.87 inference(skolemize,[status(sab)],[147])).
% 0.98/0.87 tff(149,plain,
% 0.98/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.98/0.88 tff(150,plain,
% 0.98/0.88 ((~![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)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(151,plain,
% 0.98/0.88 (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))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.98/0.88 tff(152,plain,
% 0.98/0.88 ((~(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))),
% 0.98/0.88 inference(tautology,[status(thm)],[])).
% 0.98/0.88 tff(153,plain,
% 0.98/0.88 ((~(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))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[152, 123])).
% 0.98/0.88 tff(154,plain,
% 0.98/0.88 (m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[153, 151])).
% 0.98/0.88 tff(155,plain,
% 0.98/0.88 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(156,plain,
% 0.98/0.88 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[155, 149])).
% 0.98/0.88 tff(157,plain,
% 0.98/0.88 (^[A: $i] : refl((~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(158,plain,
% 0.98/0.88 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[157])).
% 0.98/0.88 tff(159,plain,
% 0.98/0.88 (^[A: $i] : rewrite((v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(160,plain,
% 0.98/0.88 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[159])).
% 0.98/0.88 tff(161,plain,
% 0.98/0.88 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(162,axiom,(![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 0.98/0.88 tff(163,plain,
% 0.98/0.88 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.98/0.88 tff(164,plain,(
% 0.98/0.88 ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.98/0.88 inference(skolemize,[status(sab)],[163])).
% 0.98/0.88 tff(165,plain,
% 0.98/0.88 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.98/0.88 tff(166,plain,
% 0.98/0.88 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.98/0.88 tff(167,plain,
% 0.98/0.88 ((~![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))) | (~((~v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(168,plain,
% 0.98/0.88 (~((~v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.98/0.88 tff(169,plain,
% 0.98/0.88 (((~v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(tautology,[status(thm)],[])).
% 0.98/0.88 tff(170,plain,
% 0.98/0.88 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.98/0.88 tff(171,plain,
% 0.98/0.88 ((~(m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(tautology,[status(thm)],[])).
% 0.98/0.88 tff(172,plain,
% 0.98/0.88 ((~(m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.98/0.88 tff(173,plain,
% 0.98/0.88 (m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[172, 156])).
% 0.98/0.88 tff(174,plain,
% 0.98/0.88 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl(((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(175,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[174])).
% 0.98/0.88 tff(176,plain,
% 0.98/0.88 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) <=> (~((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> (~(~((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))))), rewrite((~(~((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))) <=> ((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> ((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> (((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite((((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(177,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[176])).
% 0.98/0.88 tff(178,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(179,plain,
% 0.98/0.88 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : rewrite(((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(180,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[179])).
% 0.98/0.88 tff(181,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_relset_1')).
% 0.98/0.88 tff(182,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.98/0.88 tff(183,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.98/0.88 tff(184,plain,(
% 0.98/0.88 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[183])).
% 0.98/0.88 tff(185,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.98/0.88 tff(186,plain,
% 0.98/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[185, 175])).
% 0.98/0.88 tff(187,plain,
% 0.98/0.88 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(188,plain,
% 0.98/0.88 (((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), 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_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(189,plain,
% 0.98/0.88 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), 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_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[188])).
% 0.98/0.88 tff(190,plain,
% 0.98/0.88 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), 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_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))),
% 0.98/0.88 inference(transitivity,[status(thm)],[189, 187])).
% 0.98/0.88 tff(191,plain,
% 0.98/0.88 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), 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_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(192,plain,
% 0.98/0.88 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.98/0.88 tff(193,plain,
% 0.98/0.88 (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[192, 186, 173, 154])).
% 0.98/0.88 tff(194,plain,
% 0.98/0.88 (k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))),
% 0.98/0.88 inference(symmetry,[status(thm)],[193])).
% 0.98/0.88 tff(195,plain,
% 0.98/0.88 (((~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)))) | v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(tautology,[status(thm)],[])).
% 0.98/0.88 tff(196,plain,
% 0.98/0.88 (v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[195, 121])).
% 0.98/0.88 tff(197,plain,
% 0.98/0.88 (((~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)))) | v1_funct_1(k6_autgroup(A!0, B!1))),
% 0.98/0.88 inference(tautology,[status(thm)],[])).
% 0.98/0.88 tff(198,plain,
% 0.98/0.88 (v1_funct_1(k6_autgroup(A!0, B!1))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[197, 121])).
% 0.98/0.88 tff(199,plain,
% 0.98/0.88 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(200,plain,
% 0.98/0.88 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[199])).
% 0.98/0.88 tff(201,plain,
% 0.98/0.88 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(202,plain,
% 0.98/0.88 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(203,plain,
% 0.98/0.88 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[202])).
% 0.98/0.88 tff(204,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 0.98/0.88 tff(205,plain,
% 0.98/0.88 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.98/0.88 tff(206,plain,
% 0.98/0.88 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.98/0.88 tff(207,plain,(
% 0.98/0.88 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[206])).
% 0.98/0.88 tff(208,plain,
% 0.98/0.88 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.98/0.88 tff(209,plain,
% 0.98/0.88 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(210,plain,
% 0.98/0.88 (((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0))) <=> ((~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(211,plain,
% 0.98/0.88 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[210])).
% 0.98/0.88 tff(212,plain,
% 0.98/0.88 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.88 inference(transitivity,[status(thm)],[211, 209])).
% 0.98/0.88 tff(213,plain,
% 0.98/0.88 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(214,plain,
% 0.98/0.88 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.98/0.88 tff(215,plain,
% 0.98/0.88 (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[214, 32, 29, 208])).
% 0.98/0.88 tff(216,plain,
% 0.98/0.88 (g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)) = A!0),
% 0.98/0.88 inference(symmetry,[status(thm)],[215])).
% 0.98/0.88 tff(217,plain,
% 0.98/0.88 (k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = k4_autgroup(A!0)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(218,plain,
% 0.98/0.88 (k4_autgroup(A!0) = k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(symmetry,[status(thm)],[217])).
% 0.98/0.88 tff(219,plain,
% 0.98/0.88 (u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = u1_struct_0(A!0)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(220,plain,
% 0.98/0.88 (u1_struct_0(A!0) = u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(symmetry,[status(thm)],[219])).
% 0.98/0.88 tff(221,plain,
% 0.98/0.88 (k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(222,plain,
% 0.98/0.88 (k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0))),
% 0.98/0.88 inference(symmetry,[status(thm)],[221])).
% 0.98/0.88 tff(223,plain,
% 0.98/0.88 (^[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))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(224,plain,
% 0.98/0.88 (![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)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[223])).
% 0.98/0.88 tff(225,plain,
% 0.98/0.88 (^[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)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(226,plain,
% 0.98/0.88 (![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)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[225])).
% 0.98/0.88 tff(227,plain,
% 0.98/0.88 (![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))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(228,plain,
% 0.98/0.88 (^[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))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(229,plain,
% 0.98/0.88 (![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))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[228])).
% 0.98/0.88 tff(230,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')).
% 0.98/0.88 tff(231,plain,
% 0.98/0.88 (![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))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.98/0.88 tff(232,plain,
% 0.98/0.88 (![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))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.98/0.88 tff(233,plain,(
% 0.98/0.88 ![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))))),
% 0.98/0.88 inference(skolemize,[status(sab)],[232])).
% 0.98/0.88 tff(234,plain,
% 0.98/0.88 (![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)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.98/0.88 tff(235,plain,
% 0.98/0.88 (![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)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[234, 224])).
% 0.98/0.88 tff(236,plain,
% 0.98/0.88 (((~![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) | (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)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(237,plain,
% 0.98/0.88 ((~![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)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(238,plain,
% 0.98/0.88 ((~![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))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.98/0.88 tff(239,plain,
% 0.98/0.88 (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[238, 33, 32, 31, 30, 29, 235])).
% 0.98/0.88 tff(240,plain,
% 0.98/0.88 (k6_partfun1(u1_struct_0(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))),
% 0.98/0.88 inference(symmetry,[status(thm)],[239])).
% 0.98/0.88 tff(241,plain,
% 0.98/0.88 (k6_partfun1(u1_struct_0(A!0)) = k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0))),
% 0.98/0.88 inference(transitivity,[status(thm)],[240, 222])).
% 0.98/0.88 tff(242,plain,
% 0.98/0.88 (m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[241, 220, 220, 218])).
% 0.98/0.88 tff(243,plain,
% 0.98/0.88 (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.98/0.88 inference(symmetry,[status(thm)],[242])).
% 0.98/0.88 tff(244,plain,
% 0.98/0.88 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> l1_group_1(A!0)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(245,plain,
% 0.98/0.88 (l1_group_1(A!0) <=> l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(symmetry,[status(thm)],[244])).
% 0.98/0.88 tff(246,plain,
% 0.98/0.88 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[29, 245])).
% 0.98/0.88 tff(247,plain,
% 0.98/0.88 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_1(A!0)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(248,plain,
% 0.98/0.88 (v4_group_1(A!0) <=> v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(symmetry,[status(thm)],[247])).
% 0.98/0.88 tff(249,plain,
% 0.98/0.88 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[30, 248])).
% 0.98/0.88 tff(250,plain,
% 0.98/0.88 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_group_1(A!0)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(251,plain,
% 0.98/0.88 (v3_group_1(A!0) <=> v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(symmetry,[status(thm)],[250])).
% 0.98/0.88 tff(252,plain,
% 0.98/0.88 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[31, 251])).
% 0.98/0.88 tff(253,plain,
% 0.98/0.88 (v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_1(A!0)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.88 tff(254,plain,
% 0.98/0.88 (v1_group_1(A!0) <=> v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(symmetry,[status(thm)],[253])).
% 0.98/0.88 tff(255,plain,
% 0.98/0.88 (v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[32, 254])).
% 0.98/0.88 tff(256,plain,
% 0.98/0.88 (m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[219])).
% 0.98/0.88 tff(257,plain,
% 0.98/0.88 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) <=> m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.88 inference(symmetry,[status(thm)],[256])).
% 0.98/0.88 tff(258,plain,
% 0.98/0.88 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(259,plain,
% 0.98/0.88 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[258])).
% 0.98/0.88 tff(260,plain,
% 0.98/0.88 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(261,plain,
% 0.98/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[260])).
% 0.98/0.88 tff(262,plain,
% 0.98/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(263,plain,
% 0.98/0.88 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(264,plain,
% 0.98/0.88 (![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[263])).
% 0.98/0.88 tff(265,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_group_1')).
% 0.98/0.88 tff(266,plain,
% 0.98/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.98/0.88 tff(267,plain,
% 0.98/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.98/0.88 tff(268,plain,(
% 0.98/0.88 ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[267])).
% 0.98/0.88 tff(269,plain,
% 0.98/0.88 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.98/0.88 tff(270,plain,
% 0.98/0.88 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[269, 259])).
% 0.98/0.88 tff(271,plain,
% 0.98/0.88 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(272,plain,
% 0.98/0.88 ((v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(273,plain,
% 0.98/0.88 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[272])).
% 0.98/0.89 tff(274,plain,
% 0.98/0.89 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[273, 271])).
% 0.98/0.89 tff(275,plain,
% 0.98/0.89 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(276,plain,
% 0.98/0.89 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.98/0.89 tff(277,plain,
% 0.98/0.89 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[276, 33, 29, 270])).
% 0.98/0.89 tff(278,plain,
% 0.98/0.89 (m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[277, 257])).
% 0.98/0.89 tff(279,plain,
% 0.98/0.89 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_struct_0(A!0)),
% 0.98/0.89 inference(monotonicity,[status(thm)],[216])).
% 0.98/0.89 tff(280,plain,
% 0.98/0.89 (v3_struct_0(A!0) <=> v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.89 inference(symmetry,[status(thm)],[279])).
% 0.98/0.89 tff(281,plain,
% 0.98/0.89 ((~v3_struct_0(A!0)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[280])).
% 0.98/0.89 tff(282,plain,
% 0.98/0.89 (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[33, 281])).
% 0.98/0.89 tff(283,plain,
% 0.98/0.89 (((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(284,plain,
% 0.98/0.89 ((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(285,plain,
% 0.98/0.89 ((~![A: $i, B: $i] : (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))) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.98/0.89 tff(286,plain,
% 0.98/0.89 (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[285, 108])).
% 0.98/0.89 tff(287,plain,
% 0.98/0.89 (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[286, 282, 278, 255, 252, 249, 246])).
% 0.98/0.89 tff(288,plain,
% 0.98/0.89 (m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[287, 243])).
% 0.98/0.89 tff(289,plain,
% 0.98/0.89 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(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), k4_autgroup(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))))))) | (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(290,plain,
% 0.98/0.89 (((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(291,plain,
% 0.98/0.89 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(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), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[290])).
% 0.98/0.89 tff(292,plain,
% 0.98/0.89 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(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), k4_autgroup(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))))))) | (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.98/0.89 inference(transitivity,[status(thm)],[291, 289])).
% 0.98/0.89 tff(293,plain,
% 0.98/0.89 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(294,plain,
% 0.98/0.89 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))))))) | (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.98/0.89 tff(295,plain,
% 0.98/0.89 ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[294, 95])).
% 0.98/0.89 tff(296,plain,
% 0.98/0.89 (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[295, 288])).
% 0.98/0.89 tff(297,plain,
% 0.98/0.89 (((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.89 inference(tautology,[status(thm)],[])).
% 0.98/0.89 tff(298,plain,
% 0.98/0.89 (v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.98/0.89 tff(299,plain,
% 0.98/0.89 (^[A: $i] : refl((k6_partfun1(A) = k6_relat_1(A)) <=> (k6_partfun1(A) = k6_relat_1(A)))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(300,plain,
% 0.98/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[299])).
% 0.98/0.89 tff(301,plain,
% 0.98/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(302,axiom,(![A: $i] : (k6_partfun1(A) = k6_relat_1(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 0.98/0.89 tff(303,plain,
% 0.98/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.98/0.89 tff(304,plain,(
% 0.98/0.89 ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.98/0.89 inference(skolemize,[status(sab)],[303])).
% 0.98/0.89 tff(305,plain,
% 0.98/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.98/0.89 tff(306,plain,
% 0.98/0.89 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(307,plain,
% 0.98/0.89 (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.98/0.89 tff(308,plain,
% 0.98/0.89 (k6_relat_1(u1_struct_0(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 0.98/0.89 inference(symmetry,[status(thm)],[307])).
% 0.98/0.89 tff(309,plain,
% 0.98/0.89 (v1_funct_1(k6_relat_1(u1_struct_0(A!0))) <=> v1_funct_1(k6_partfun1(u1_struct_0(A!0)))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[308])).
% 0.98/0.89 tff(310,plain,
% 0.98/0.89 (^[A: $i] : refl((~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))) <=> (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(311,plain,
% 0.98/0.89 (![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))) <=> ![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[310])).
% 0.98/0.89 tff(312,plain,
% 0.98/0.89 (^[A: $i] : rewrite((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A))) <=> (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(313,plain,
% 0.98/0.89 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A))) <=> ![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[312])).
% 0.98/0.89 tff(314,plain,
% 0.98/0.89 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A))) <=> ![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(315,plain,
% 0.98/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)))), ((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) <=> ((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))))), rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))), ((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A))))), (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) <=> ((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))))), rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))), (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A))))), ((((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> ((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))))), rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))), ((((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(316,plain,
% 0.98/0.89 (![A: $i] : (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> ![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[315])).
% 0.98/0.89 tff(317,axiom,(![A: $i] : (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_partfun1')).
% 0.98/0.89 tff(318,plain,
% 0.98/0.89 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.98/0.89 tff(319,plain,
% 0.98/0.89 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.98/0.89 tff(320,plain,(
% 0.98/0.89 ![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.98/0.89 inference(skolemize,[status(sab)],[319])).
% 0.98/0.89 tff(321,plain,
% 0.98/0.89 (![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.98/0.89 tff(322,plain,
% 0.98/0.89 (![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[321, 311])).
% 0.98/0.89 tff(323,plain,
% 0.98/0.89 ((~![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))) | (~((~v1_relat_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v3_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v4_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v8_relat_2(k6_relat_1(u1_struct_0(A!0))))))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(324,plain,
% 0.98/0.89 (~((~v1_relat_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v3_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v4_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v8_relat_2(k6_relat_1(u1_struct_0(A!0)))))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.98/0.89 tff(325,plain,
% 0.98/0.89 (((~v1_relat_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v3_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v4_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v8_relat_2(k6_relat_1(u1_struct_0(A!0))))) | v1_funct_1(k6_relat_1(u1_struct_0(A!0)))),
% 0.98/0.89 inference(tautology,[status(thm)],[])).
% 0.98/0.89 tff(326,plain,
% 0.98/0.89 (v1_funct_1(k6_relat_1(u1_struct_0(A!0)))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.98/0.89 tff(327,plain,
% 0.98/0.89 (v1_funct_1(k6_partfun1(u1_struct_0(A!0)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[326, 309])).
% 0.98/0.89 tff(328,plain,
% 0.98/0.89 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(329,plain,
% 0.98/0.89 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[328])).
% 0.98/0.89 tff(330,plain,
% 0.98/0.89 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(331,plain,
% 0.98/0.89 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[330])).
% 0.98/0.89 tff(332,plain,
% 0.98/0.89 (![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)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(333,plain,
% 0.98/0.89 (^[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)))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(334,plain,
% 0.98/0.89 (![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)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[333])).
% 0.98/0.89 tff(335,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')).
% 0.98/0.89 tff(336,plain,
% 0.98/0.89 (![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)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.98/0.89 tff(337,plain,
% 0.98/0.89 (![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)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.98/0.89 tff(338,plain,(
% 0.98/0.89 ![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)))),
% 0.98/0.89 inference(skolemize,[status(sab)],[337])).
% 0.98/0.89 tff(339,plain,
% 0.98/0.89 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[338, 331])).
% 0.98/0.89 tff(340,plain,
% 0.98/0.89 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[339, 329])).
% 0.98/0.89 tff(341,plain,
% 0.98/0.89 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(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)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(342,plain,
% 0.98/0.89 ((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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(343,plain,
% 0.98/0.89 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[342])).
% 0.98/0.90 tff(344,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))))),
% 0.98/0.90 inference(transitivity,[status(thm)],[343, 341])).
% 0.98/0.90 tff(345,plain,
% 0.98/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(346,plain,
% 0.98/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.98/0.90 tff(347,plain,
% 0.98/0.90 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[346, 340, 75, 327, 298, 173, 198, 196, 154])).
% 0.98/0.90 tff(348,plain,
% 0.98/0.90 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[239])).
% 0.98/0.90 tff(349,plain,
% 0.98/0.90 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1)),
% 0.98/0.90 inference(transitivity,[status(thm)],[348, 347, 194, 142])).
% 0.98/0.90 tff(350,plain,
% 0.98/0.90 (((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))) | (~(k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1)))) | (k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1))),
% 0.98/0.90 inference(tautology,[status(thm)],[])).
% 0.98/0.90 tff(351,plain,
% 0.98/0.90 (k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k6_autgroup(A!0, B!1)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[350, 140])).
% 0.98/0.90 tff(352,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(353,plain,
% 0.98/0.90 (((k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_partfun1(u1_struct_0(A!0)), 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_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(354,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[353])).
% 0.98/0.90 tff(355,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))),
% 0.98/0.90 inference(transitivity,[status(thm)],[354, 352])).
% 0.98/0.90 tff(356,plain,
% 0.98/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(357,plain,
% 0.98/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.98/0.90 tff(358,plain,
% 0.98/0.90 (k7_relset_1(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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[357, 186, 173, 154])).
% 0.98/0.90 tff(359,plain,
% 0.98/0.90 (k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))) = k7_relset_1(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_partfun1(u1_struct_0(A!0)))),
% 0.98/0.90 inference(symmetry,[status(thm)],[358])).
% 0.98/0.90 tff(360,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(361,plain,
% 0.98/0.90 ((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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(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))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(362,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(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))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[361])).
% 0.98/0.90 tff(363,plain,
% 0.98/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(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))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))))),
% 0.98/0.90 inference(transitivity,[status(thm)],[362, 360])).
% 0.98/0.90 tff(364,plain,
% 0.98/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(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))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(365,plain,
% 0.98/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), 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))) | (~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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0))))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.98/0.90 tff(366,plain,
% 0.98/0.90 (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_partfun1(u1_struct_0(A!0))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_partfun1(u1_struct_0(A!0)))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[365, 340, 75, 327, 298, 173, 198, 196, 154])).
% 0.98/0.90 tff(367,plain,
% 0.98/0.90 (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, k2_group_1(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_partfun1(u1_struct_0(A!0)))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[239])).
% 0.98/0.90 tff(368,plain,
% 0.98/0.90 (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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1)),
% 0.98/0.90 inference(transitivity,[status(thm)],[367, 366, 359, 351])).
% 0.98/0.90 tff(369,assumption,(~(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))), introduced(assumption)).
% 0.98/0.90 tff(370,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[369, 368])).
% 0.98/0.90 tff(371,plain,(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(372,plain,
% 0.98/0.90 ((~(~((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(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, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(373,plain,
% 0.98/0.90 (((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(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, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1)))))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(374,plain,
% 0.98/0.90 ((~((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(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, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[373])).
% 0.98/0.90 tff(375,plain,
% 0.98/0.90 ((~((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(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, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1))))),
% 0.98/0.90 inference(transitivity,[status(thm)],[374, 372])).
% 0.98/0.90 tff(376,plain,
% 0.98/0.90 (~((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1)))),
% 0.98/0.90 inference(or_elim,[status(thm)],[109])).
% 0.98/0.90 tff(377,plain,
% 0.98/0.90 ((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(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, k2_group_1(A!0))) = k6_autgroup(A!0, B!1)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.98/0.91 tff(378,plain,
% 0.98/0.91 (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, B!1))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[377, 371])).
% 0.98/0.91 tff(379,plain,
% 0.98/0.91 ($false),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[378, 349])).
% 0.98/0.91 % SZS output end Proof
%------------------------------------------------------------------------------