TSTP Solution File: GRP625+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP625+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:28:54 EDT 2022
% Result : Theorem 2.04s 1.54s
% Output : Proof 2.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP625+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 18:40:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 2.04/1.54 % SZS status Theorem
% 2.04/1.54 % SZS output start Proof
% 2.04/1.54 tff(k2_group_3_type, type, (
% 2.04/1.54 k2_group_3: ( $i * $i * $i ) > $i)).
% 2.04/1.54 tff(k2_group_1_type, type, (
% 2.04/1.54 k2_group_1: $i > $i)).
% 2.04/1.54 tff(tptp_fun_A_0_type, type, (
% 2.04/1.54 tptp_fun_A_0: $i)).
% 2.04/1.54 tff(tptp_fun_E_2_type, type, (
% 2.04/1.54 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 2.04/1.54 tff(k6_relat_1_type, type, (
% 2.04/1.54 k6_relat_1: $i > $i)).
% 2.04/1.54 tff(u1_struct_0_type, type, (
% 2.04/1.54 u1_struct_0: $i > $i)).
% 2.04/1.54 tff(k8_funct_2_type, type, (
% 2.04/1.54 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 2.04/1.54 tff(k1_group_1_type, type, (
% 2.04/1.54 k1_group_1: ( $i * $i * $i ) > $i)).
% 2.04/1.54 tff(k3_group_1_type, type, (
% 2.04/1.54 k3_group_1: ( $i * $i ) > $i)).
% 2.04/1.54 tff(m1_subset_1_type, type, (
% 2.04/1.54 m1_subset_1: ( $i * $i ) > $o)).
% 2.04/1.54 tff(r2_hidden_type, type, (
% 2.04/1.54 r2_hidden: ( $i * $i ) > $o)).
% 2.04/1.54 tff(k4_autgroup_type, type, (
% 2.04/1.54 k4_autgroup: $i > $i)).
% 2.04/1.54 tff(tptp_fun_D_1_type, type, (
% 2.04/1.54 tptp_fun_D_1: ( $i * $i ) > $i)).
% 2.04/1.54 tff(m2_fraenkel_type, type, (
% 2.04/1.54 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 2.04/1.54 tff(k1_fraenkel_type, type, (
% 2.04/1.54 k1_fraenkel: ( $i * $i ) > $i)).
% 2.04/1.54 tff(k1_funct_2_type, type, (
% 2.04/1.54 k1_funct_2: ( $i * $i ) > $i)).
% 2.04/1.54 tff(v1_xboole_0_type, type, (
% 2.04/1.54 v1_xboole_0: $i > $o)).
% 2.04/1.54 tff(l1_struct_0_type, type, (
% 2.04/1.54 l1_struct_0: $i > $o)).
% 2.04/1.54 tff(l1_group_1_type, type, (
% 2.04/1.54 l1_group_1: $i > $o)).
% 2.04/1.54 tff(v4_group_1_type, type, (
% 2.04/1.54 v4_group_1: $i > $o)).
% 2.04/1.54 tff(v3_group_1_type, type, (
% 2.04/1.54 v3_group_1: $i > $o)).
% 2.04/1.54 tff(v1_group_1_type, type, (
% 2.04/1.54 v1_group_1: $i > $o)).
% 2.04/1.54 tff(v3_struct_0_type, type, (
% 2.04/1.54 v3_struct_0: $i > $o)).
% 2.04/1.54 tff(k6_partfun1_type, type, (
% 2.04/1.54 k6_partfun1: $i > $i)).
% 2.04/1.54 tff(m1_fraenkel_type, type, (
% 2.04/1.54 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 2.04/1.54 tff(m2_relset_1_type, type, (
% 2.04/1.54 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.04/1.54 tff(v1_partfun1_type, type, (
% 2.04/1.54 v1_partfun1: ( $i * $i * $i ) > $o)).
% 2.04/1.54 tff(v1_funct_1_type, type, (
% 2.04/1.54 v1_funct_1: $i > $o)).
% 2.04/1.54 tff(v8_relat_2_type, type, (
% 2.04/1.54 v8_relat_2: $i > $o)).
% 2.04/1.54 tff(v4_relat_2_type, type, (
% 2.04/1.54 v4_relat_2: $i > $o)).
% 2.04/1.54 tff(v3_relat_2_type, type, (
% 2.04/1.54 v3_relat_2: $i > $o)).
% 2.04/1.54 tff(v1_relat_1_type, type, (
% 2.04/1.54 v1_relat_1: $i > $o)).
% 2.04/1.54 tff(v1_relat_2_type, type, (
% 2.04/1.54 v1_relat_2: $i > $o)).
% 2.04/1.54 tff(v1_funct_2_type, type, (
% 2.04/1.54 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.04/1.54 tff(m1_relset_1_type, type, (
% 2.04/1.54 m1_relset_1: ( $i * $i * $i ) > $o)).
% 2.04/1.54 tff(k1_xboole_0_type, type, (
% 2.04/1.54 k1_xboole_0: $i)).
% 2.04/1.54 tff(tptp_fun_D_4_type, type, (
% 2.04/1.54 tptp_fun_D_4: ( $i * $i ) > $i)).
% 2.04/1.54 tff(tptp_fun_C_3_type, type, (
% 2.04/1.54 tptp_fun_C_3: ( $i * $i ) > $i)).
% 2.04/1.54 tff(tptp_fun_E_5_type, type, (
% 2.04/1.54 tptp_fun_E_5: ( $i * $i * $i ) > $i)).
% 2.04/1.54 tff(tptp_fun_C_6_type, type, (
% 2.04/1.54 tptp_fun_C_6: ( $i * $i ) > $i)).
% 2.04/1.54 tff(v2_group_1_type, type, (
% 2.04/1.54 v2_group_1: $i > $o)).
% 2.04/1.54 tff(k1_funct_1_type, type, (
% 2.04/1.54 k1_funct_1: ( $i * $i ) > $i)).
% 2.04/1.54 tff(1,plain,
% 2.04/1.54 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(2,plain,
% 2.04/1.54 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[1])).
% 2.04/1.54 tff(3,plain,
% 2.04/1.54 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(4,plain,
% 2.04/1.54 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(5,plain,
% 2.04/1.54 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[4])).
% 2.04/1.54 tff(6,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 2.04/1.54 tff(7,plain,
% 2.04/1.54 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.04/1.54 tff(8,plain,
% 2.04/1.54 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.04/1.54 tff(9,plain,(
% 2.04/1.54 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(skolemize,[status(sab)],[8])).
% 2.04/1.54 tff(10,plain,
% 2.04/1.54 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.04/1.54 tff(11,plain,
% 2.04/1.54 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(12,plain,
% 2.04/1.54 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(13,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_autgroup')).
% 2.04/1.54 tff(14,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.04/1.54 tff(15,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[14, 11])).
% 2.04/1.54 tff(16,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[15, 11])).
% 2.04/1.54 tff(17,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[16, 11])).
% 2.04/1.54 tff(18,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[17, 11])).
% 2.04/1.54 tff(19,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[18, 11])).
% 2.04/1.54 tff(20,plain,
% 2.04/1.54 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m2_fraenkel(k6_partfun1(u1_struct_0(A)), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[19, 11])).
% 2.04/1.54 tff(21,plain,(
% 2.04/1.54 ~((~((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))) | m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 2.04/1.54 inference(skolemize,[status(sab)],[20])).
% 2.04/1.54 tff(22,plain,
% 2.04/1.54 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)),
% 2.04/1.54 inference(or_elim,[status(thm)],[21])).
% 2.04/1.54 tff(23,plain,
% 2.04/1.54 (l1_group_1(A!0)),
% 2.04/1.54 inference(and_elim,[status(thm)],[22])).
% 2.04/1.54 tff(24,plain,
% 2.04/1.54 (((~![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)))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(25,plain,
% 2.04/1.54 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 2.04/1.54 inference(quant_inst,[status(thm)],[])).
% 2.04/1.54 tff(26,plain,
% 2.04/1.54 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.04/1.54 tff(27,plain,
% 2.04/1.54 (l1_struct_0(A!0)),
% 2.04/1.54 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 2.04/1.54 tff(28,plain,
% 2.04/1.54 (^[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))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(29,plain,
% 2.04/1.54 (![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)))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[28])).
% 2.04/1.54 tff(30,plain,
% 2.04/1.54 (^[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)))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(31,plain,
% 2.04/1.54 (![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)))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[30])).
% 2.04/1.54 tff(32,plain,
% 2.04/1.54 (![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))))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(33,plain,
% 2.04/1.54 (^[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)))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(34,plain,
% 2.04/1.54 (![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))))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[33])).
% 2.04/1.54 tff(35,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 2.04/1.54 tff(36,plain,
% 2.04/1.54 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.04/1.54 tff(37,plain,
% 2.04/1.54 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[36, 32])).
% 2.04/1.54 tff(38,plain,(
% 2.04/1.54 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.04/1.54 inference(skolemize,[status(sab)],[37])).
% 2.04/1.54 tff(39,plain,
% 2.04/1.54 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[38, 31])).
% 2.04/1.54 tff(40,plain,
% 2.04/1.54 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[39, 29])).
% 2.04/1.54 tff(41,plain,
% 2.04/1.54 (~v3_struct_0(A!0)),
% 2.04/1.54 inference(and_elim,[status(thm)],[22])).
% 2.04/1.54 tff(42,plain,
% 2.04/1.54 (((~![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))))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(43,plain,
% 2.04/1.54 ((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))))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(44,plain,
% 2.04/1.54 (((~![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)))))),
% 2.04/1.54 inference(monotonicity,[status(thm)],[43])).
% 2.04/1.54 tff(45,plain,
% 2.04/1.54 (((~![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))))),
% 2.04/1.54 inference(transitivity,[status(thm)],[44, 42])).
% 2.04/1.54 tff(46,plain,
% 2.04/1.54 ((~![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)))),
% 2.04/1.54 inference(quant_inst,[status(thm)],[])).
% 2.04/1.54 tff(47,plain,
% 2.04/1.54 ((~![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)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[46, 45])).
% 2.04/1.54 tff(48,plain,
% 2.04/1.54 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 2.04/1.54 inference(unit_resolution,[status(thm)],[47, 41, 40])).
% 2.04/1.54 tff(49,plain,
% 2.04/1.54 (~v1_xboole_0(u1_struct_0(A!0))),
% 2.04/1.54 inference(unit_resolution,[status(thm)],[48, 27])).
% 2.04/1.54 tff(50,plain,
% 2.04/1.54 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(51,plain,
% 2.04/1.54 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[50])).
% 2.04/1.54 tff(52,plain,
% 2.04/1.54 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(53,plain,
% 2.04/1.54 (^[A: $i, B: $i] : rewrite(((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))))),
% 2.04/1.54 inference(bind,[status(th)],[])).
% 2.04/1.54 tff(54,plain,
% 2.04/1.54 (![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(quant_intro,[status(thm)],[53])).
% 2.04/1.54 tff(55,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_fraenkel')).
% 2.04/1.54 tff(56,plain,
% 2.04/1.54 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.04/1.54 tff(57,plain,
% 2.04/1.54 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[56, 52])).
% 2.04/1.54 tff(58,plain,(
% 2.04/1.54 ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(skolemize,[status(sab)],[57])).
% 2.04/1.54 tff(59,plain,
% 2.04/1.54 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[58, 51])).
% 2.04/1.54 tff(60,plain,
% 2.04/1.54 (((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.54 inference(rewrite,[status(thm)],[])).
% 2.04/1.54 tff(61,plain,
% 2.04/1.54 ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.54 inference(quant_inst,[status(thm)],[])).
% 2.04/1.54 tff(62,plain,
% 2.04/1.54 ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.54 inference(modus_ponens,[status(thm)],[61, 60])).
% 2.04/1.54 tff(63,plain,
% 2.04/1.54 (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.54 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 2.04/1.54 tff(64,plain,
% 2.04/1.54 (k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.54 inference(symmetry,[status(thm)],[63])).
% 2.04/1.54 tff(65,plain,
% 2.04/1.54 (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.54 inference(monotonicity,[status(thm)],[64])).
% 2.04/1.54 tff(66,plain,
% 2.04/1.54 (m1_fraenkel(k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[64])).
% 2.04/1.55 tff(67,plain,
% 2.04/1.55 (m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_fraenkel(k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(symmetry,[status(thm)],[66])).
% 2.04/1.55 tff(68,plain,
% 2.04/1.55 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B)) <=> (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(69,plain,
% 2.04/1.55 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[68])).
% 2.04/1.55 tff(70,plain,
% 2.04/1.55 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(71,plain,
% 2.04/1.55 (^[A: $i, B: $i] : rewrite(((~v1_xboole_0(B)) => m1_fraenkel(k1_fraenkel(A, B), A, B)) <=> (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(72,plain,
% 2.04/1.55 (![A: $i, B: $i] : ((~v1_xboole_0(B)) => m1_fraenkel(k1_fraenkel(A, B), A, B)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[71])).
% 2.04/1.55 tff(73,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(B)) => m1_fraenkel(k1_fraenkel(A, B), A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_fraenkel')).
% 2.04/1.55 tff(74,plain,
% 2.04/1.55 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.04/1.55 tff(75,plain,
% 2.04/1.55 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[74, 70])).
% 2.04/1.55 tff(76,plain,(
% 2.04/1.55 ![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(skolemize,[status(sab)],[75])).
% 2.04/1.55 tff(77,plain,
% 2.04/1.55 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[76, 69])).
% 2.04/1.55 tff(78,plain,
% 2.04/1.55 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))) | (v1_xboole_0(u1_struct_0(A!0)) | m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))) | v1_xboole_0(u1_struct_0(A!0)) | m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(79,plain,
% 2.04/1.55 ((~![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))) | (v1_xboole_0(u1_struct_0(A!0)) | m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(80,plain,
% 2.04/1.55 ((~![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))) | v1_xboole_0(u1_struct_0(A!0)) | m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.04/1.55 tff(81,plain,
% 2.04/1.55 (m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[80, 77, 49])).
% 2.04/1.55 tff(82,plain,
% 2.04/1.55 (m1_fraenkel(k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[81, 67])).
% 2.04/1.55 tff(83,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(84,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[83])).
% 2.04/1.55 tff(85,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(86,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[85])).
% 2.04/1.55 tff(87,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(88,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[87])).
% 2.04/1.55 tff(89,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 2.04/1.55 inference(transitivity,[status(thm)],[88, 86])).
% 2.04/1.55 tff(90,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(91,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[90])).
% 2.04/1.55 tff(92,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(93,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(94,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[93])).
% 2.04/1.55 tff(95,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 2.04/1.55 tff(96,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[95, 94])).
% 2.04/1.55 tff(97,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[96, 92])).
% 2.04/1.55 tff(98,plain,(
% 2.04/1.55 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(skolemize,[status(sab)],[97])).
% 2.04/1.55 tff(99,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[98, 91])).
% 2.04/1.55 tff(100,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[99, 89])).
% 2.04/1.55 tff(101,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[100, 84])).
% 2.04/1.55 tff(102,plain,
% 2.04/1.55 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_funct_2(u1_struct_0(A!0), 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), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(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) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_funct_2(u1_struct_0(A!0), 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), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(103,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_funct_2(u1_struct_0(A!0), 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), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(104,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_funct_2(u1_struct_0(A!0), 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), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.04/1.55 tff(105,plain,
% 2.04/1.55 ((~m1_fraenkel(k1_funct_2(u1_struct_0(A!0), 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), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[104, 101, 49])).
% 2.04/1.55 tff(106,plain,
% 2.04/1.55 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[105, 82])).
% 2.04/1.55 tff(107,plain,
% 2.04/1.55 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(D, k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) | (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(108,plain,
% 2.04/1.55 (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[107, 106])).
% 2.04/1.55 tff(109,plain,
% 2.04/1.55 (^[A: $i] : refl((k6_partfun1(A) = k6_relat_1(A)) <=> (k6_partfun1(A) = k6_relat_1(A)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(110,plain,
% 2.04/1.55 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[109])).
% 2.04/1.55 tff(111,plain,
% 2.04/1.55 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(112,axiom,(![A: $i] : (k6_partfun1(A) = k6_relat_1(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 2.04/1.55 tff(113,plain,
% 2.04/1.55 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.04/1.55 tff(114,plain,(
% 2.04/1.55 ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 2.04/1.55 inference(skolemize,[status(sab)],[113])).
% 2.04/1.55 tff(115,plain,
% 2.04/1.55 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[114, 110])).
% 2.04/1.55 tff(116,plain,
% 2.04/1.55 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0)))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(117,plain,
% 2.04/1.55 (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[116, 115])).
% 2.04/1.55 tff(118,plain,
% 2.04/1.55 (k6_relat_1(u1_struct_0(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 2.04/1.55 inference(symmetry,[status(thm)],[117])).
% 2.04/1.55 tff(119,plain,
% 2.04/1.55 (m2_relset_1(k6_relat_1(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))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[118])).
% 2.04/1.55 tff(120,plain,
% 2.04/1.55 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(symmetry,[status(thm)],[119])).
% 2.04/1.55 tff(121,plain,
% 2.04/1.55 (^[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)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(122,plain,
% 2.04/1.55 (![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))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[121])).
% 2.04/1.55 tff(123,plain,
% 2.04/1.55 (^[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)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(124,plain,
% 2.04/1.55 (![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))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[123])).
% 2.04/1.55 tff(125,plain,
% 2.04/1.55 (![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))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(126,axiom,(![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 2.04/1.55 tff(127,plain,
% 2.04/1.55 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[126, 125])).
% 2.04/1.55 tff(128,plain,(
% 2.04/1.55 ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 2.04/1.55 inference(skolemize,[status(sab)],[127])).
% 2.04/1.55 tff(129,plain,
% 2.04/1.55 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[128, 124])).
% 2.04/1.55 tff(130,plain,
% 2.04/1.55 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[129, 122])).
% 2.04/1.55 tff(131,plain,
% 2.04/1.55 ((~![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)))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(132,plain,
% 2.04/1.55 (~((~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))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[131, 130])).
% 2.04/1.55 tff(133,plain,
% 2.04/1.55 (((~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))),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(134,plain,
% 2.04/1.55 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[133, 132])).
% 2.04/1.55 tff(135,plain,
% 2.04/1.55 (m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[134, 120])).
% 2.04/1.55 tff(136,plain,
% 2.04/1.55 (^[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))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(137,plain,
% 2.04/1.55 (![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)))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[136])).
% 2.04/1.55 tff(138,plain,
% 2.04/1.55 (^[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))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(139,plain,
% 2.04/1.55 (![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)))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[138])).
% 2.04/1.55 tff(140,plain,
% 2.04/1.55 (![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)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(141,plain,
% 2.04/1.55 (^[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)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(142,plain,
% 2.04/1.55 (![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)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[141])).
% 2.04/1.55 tff(143,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/sandbox/benchmark/theBenchmark.p','fc2_partfun1')).
% 2.04/1.55 tff(144,plain,
% 2.04/1.55 (![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)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.04/1.55 tff(145,plain,
% 2.04/1.55 (![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)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[144, 140])).
% 2.04/1.55 tff(146,plain,(
% 2.04/1.55 ![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)))),
% 2.04/1.55 inference(skolemize,[status(sab)],[145])).
% 2.04/1.55 tff(147,plain,
% 2.04/1.55 (![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)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[146, 139])).
% 2.04/1.55 tff(148,plain,
% 2.04/1.55 (![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)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[147, 137])).
% 2.04/1.55 tff(149,plain,
% 2.04/1.55 (((~![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_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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))))))) <=> ((~![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_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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)))))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(150,plain,
% 2.04/1.55 ((~((~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)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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))))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(151,plain,
% 2.04/1.55 (((~![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))))))) <=> ((~![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_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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)))))))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[150])).
% 2.04/1.55 tff(152,plain,
% 2.04/1.55 (((~![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))))))) <=> ((~![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_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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)))))))),
% 2.04/1.55 inference(transitivity,[status(thm)],[151, 149])).
% 2.04/1.55 tff(153,plain,
% 2.04/1.55 ((~![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))))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(154,plain,
% 2.04/1.55 ((~![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_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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))))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[153, 152])).
% 2.04/1.55 tff(155,plain,
% 2.04/1.55 (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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)))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[154, 148])).
% 2.04/1.55 tff(156,plain,
% 2.04/1.55 (((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_1(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)))),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(157,plain,
% 2.04/1.55 (v1_funct_1(k6_relat_1(u1_struct_0(A!0)))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[156, 155])).
% 2.04/1.55 tff(158,plain,
% 2.04/1.55 (v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[118])).
% 2.04/1.55 tff(159,plain,
% 2.04/1.55 (v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(symmetry,[status(thm)],[158])).
% 2.04/1.55 tff(160,plain,
% 2.04/1.55 (((~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)))) | v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(161,plain,
% 2.04/1.55 (v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[160, 132])).
% 2.04/1.55 tff(162,plain,
% 2.04/1.55 (v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[161, 159])).
% 2.04/1.55 tff(163,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(164,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[163])).
% 2.04/1.55 tff(165,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(166,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 2.04/1.55 tff(167,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[166, 165])).
% 2.04/1.55 tff(168,plain,(
% 2.04/1.55 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.04/1.55 inference(skolemize,[status(sab)],[167])).
% 2.04/1.55 tff(169,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[168, 164])).
% 2.04/1.55 tff(170,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(171,plain,
% 2.04/1.55 (m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[170, 169])).
% 2.04/1.55 tff(172,plain,
% 2.04/1.55 ((~(m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(173,plain,
% 2.04/1.55 (m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[172, 135, 171])).
% 2.04/1.55 tff(174,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B))) <=> ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(175,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[174])).
% 2.04/1.55 tff(176,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B)) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), trans(monotonicity(rewrite((v1_funct_1(C) & v1_partfun1(C, A, B)) <=> (~((~v1_funct_1(C)) | (~v1_partfun1(C, A, B))))), ((~(v1_funct_1(C) & v1_partfun1(C, A, B))) <=> (~(~((~v1_funct_1(C)) | (~v1_partfun1(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_partfun1(C, A, B))))) <=> ((~v1_funct_1(C)) | (~v1_partfun1(C, A, B)))), ((~(v1_funct_1(C) & v1_partfun1(C, A, B))) <=> ((~v1_funct_1(C)) | (~v1_partfun1(C, A, B))))), (((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B))) <=> ((~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | ((~v1_funct_1(C)) | (~v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B))))), rewrite(((~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | ((~v1_funct_1(C)) | (~v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B))) <=> ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))), (((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B))) <=> ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(177,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[176])).
% 2.04/1.55 tff(178,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(179,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_partfun1(C, A, B)) => (v1_funct_1(C) & v1_funct_2(C, A, B))) <=> ((~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (v1_funct_1(C) & v1_funct_2(C, A, B)))), ((m1_relset_1(C, A, B) => ((v1_funct_1(C) & v1_partfun1(C, A, B)) => (v1_funct_1(C) & v1_funct_2(C, A, B)))) <=> (m1_relset_1(C, A, B) => ((~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (v1_funct_1(C) & v1_funct_2(C, A, B)))))), rewrite((m1_relset_1(C, A, B) => ((~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (v1_funct_1(C) & v1_funct_2(C, A, B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))), ((m1_relset_1(C, A, B) => ((v1_funct_1(C) & v1_partfun1(C, A, B)) => (v1_funct_1(C) & v1_funct_2(C, A, B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(180,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => ((v1_funct_1(C) & v1_partfun1(C, A, B)) => (v1_funct_1(C) & v1_funct_2(C, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[179])).
% 2.04/1.55 tff(181,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => ((v1_funct_1(C) & v1_partfun1(C, A, B)) => (v1_funct_1(C) & v1_funct_2(C, A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_funct_2')).
% 2.04/1.55 tff(182,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[181, 180])).
% 2.04/1.55 tff(183,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[182, 178])).
% 2.04/1.55 tff(184,plain,(
% 2.04/1.55 ![A: $i, B: $i, C: $i] : ((v1_funct_1(C) & v1_funct_2(C, A, B)) | (~(v1_funct_1(C) & v1_partfun1(C, A, B))) | (~m1_relset_1(C, A, B)))),
% 2.04/1.55 inference(skolemize,[status(sab)],[183])).
% 2.04/1.55 tff(185,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[184, 177])).
% 2.04/1.55 tff(186,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[185, 175])).
% 2.04/1.55 tff(187,plain,
% 2.04/1.55 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | ((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(188,plain,
% 2.04/1.55 (((~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(189,plain,
% 2.04/1.55 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | ((~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | ((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[188])).
% 2.04/1.55 tff(190,plain,
% 2.04/1.55 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | ((~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 2.04/1.55 inference(transitivity,[status(thm)],[189, 187])).
% 2.04/1.55 tff(191,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | ((~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(192,plain,
% 2.04/1.55 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (~v1_partfun1(C, A, B)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[191, 190])).
% 2.04/1.55 tff(193,plain,
% 2.04/1.55 ((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[192, 186])).
% 2.04/1.55 tff(194,plain,
% 2.04/1.55 (~((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[193, 173, 157, 162])).
% 2.04/1.55 tff(195,plain,
% 2.04/1.55 (((~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(tautology,[status(thm)],[])).
% 2.04/1.55 tff(196,plain,
% 2.04/1.55 (v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[195, 194])).
% 2.04/1.55 tff(197,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : refl((r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) <=> (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(198,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[197])).
% 2.04/1.55 tff(199,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) <=> (~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> (~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))))), rewrite((~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), ((r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)))) <=> (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))))), rewrite((r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) <=> (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))), ((r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)))) <=> (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(200,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)))) <=> ![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[199])).
% 2.04/1.55 tff(201,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)))) <=> ![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(202,plain,
% 2.04/1.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))), trans(monotonicity(rewrite(((B = k1_xboole_0) => (A = k1_xboole_0)) <=> ((~(B = k1_xboole_0)) | (A = k1_xboole_0))), ((((B = k1_xboole_0) => (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B))) <=> (((~(B = k1_xboole_0)) | (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B))))), rewrite((((~(B = k1_xboole_0)) | (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B))) <=> ((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | r2_hidden(C, k1_funct_2(A, B)))), ((((B = k1_xboole_0) => (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B))) <=> ((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | r2_hidden(C, k1_funct_2(A, B))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => (((B = k1_xboole_0) => (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | r2_hidden(C, k1_funct_2(A, B)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | r2_hidden(C, k1_funct_2(A, B)))) <=> (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => (((B = k1_xboole_0) => (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B)))) <=> (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))))),
% 2.04/1.55 inference(bind,[status(th)],[])).
% 2.04/1.55 tff(203,plain,
% 2.04/1.55 (![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => (((B = k1_xboole_0) => (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B)))) <=> ![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))),
% 2.04/1.55 inference(quant_intro,[status(thm)],[202])).
% 2.04/1.55 tff(204,axiom,(![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => (((B = k1_xboole_0) => (A = k1_xboole_0)) => r2_hidden(C, k1_funct_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t11_funct_2')).
% 2.04/1.55 tff(205,plain,
% 2.04/1.56 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[204, 203])).
% 2.04/1.56 tff(206,plain,
% 2.04/1.56 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[205, 201])).
% 2.04/1.56 tff(207,plain,(
% 2.04/1.56 ![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))))),
% 2.04/1.56 inference(skolemize,[status(sab)],[206])).
% 2.04/1.56 tff(208,plain,
% 2.04/1.56 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[207, 200])).
% 2.04/1.56 tff(209,plain,
% 2.04/1.56 (![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[208, 198])).
% 2.04/1.56 tff(210,plain,
% 2.04/1.56 (((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(211,plain,
% 2.04/1.56 ((r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | $false | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(212,plain,
% 2.04/1.56 ((~$true) <=> $false),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(213,plain,
% 2.04/1.56 (((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0)) <=> $true),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(214,plain,
% 2.04/1.56 ((~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) <=> (~$true)),
% 2.04/1.56 inference(monotonicity,[status(thm)],[213])).
% 2.04/1.56 tff(215,plain,
% 2.04/1.56 ((~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) <=> $false),
% 2.04/1.56 inference(transitivity,[status(thm)],[214, 212])).
% 2.04/1.56 tff(216,plain,
% 2.04/1.56 ((r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | $false | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(monotonicity,[status(thm)],[215])).
% 2.04/1.56 tff(217,plain,
% 2.04/1.56 ((r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(transitivity,[status(thm)],[216, 211])).
% 2.04/1.56 tff(218,plain,
% 2.04/1.56 (((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 2.04/1.56 inference(monotonicity,[status(thm)],[217])).
% 2.04/1.56 tff(219,plain,
% 2.04/1.56 (((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(transitivity,[status(thm)],[218, 210])).
% 2.04/1.56 tff(220,plain,
% 2.04/1.56 ((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(quant_inst,[status(thm)],[])).
% 2.04/1.56 tff(221,plain,
% 2.04/1.56 ((~![A: $i, B: $i, C: $i] : (r2_hidden(C, k1_funct_2(A, B)) | (~m2_relset_1(C, A, B)) | (~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))) | r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[220, 219])).
% 2.04/1.56 tff(222,plain,
% 2.04/1.56 (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[221, 209])).
% 2.04/1.56 tff(223,plain,
% 2.04/1.56 (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[222, 196, 157, 135])).
% 2.04/1.56 tff(224,plain,
% 2.04/1.56 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(225,plain,
% 2.04/1.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[224])).
% 2.04/1.56 tff(226,plain,
% 2.04/1.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(227,plain,
% 2.04/1.56 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(228,plain,
% 2.04/1.56 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[227])).
% 2.04/1.56 tff(229,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 2.04/1.56 tff(230,plain,
% 2.04/1.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[229, 228])).
% 2.04/1.56 tff(231,plain,
% 2.04/1.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[230, 226])).
% 2.04/1.56 tff(232,plain,(
% 2.04/1.56 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(skolemize,[status(sab)],[231])).
% 2.04/1.56 tff(233,plain,
% 2.04/1.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[232, 225])).
% 2.04/1.56 tff(234,plain,
% 2.04/1.56 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(235,plain,
% 2.04/1.56 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(quant_inst,[status(thm)],[])).
% 2.04/1.56 tff(236,plain,
% 2.04/1.56 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[235, 234])).
% 2.04/1.56 tff(237,plain,
% 2.04/1.56 (m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[236, 233, 223])).
% 2.04/1.56 tff(238,plain,
% 2.04/1.56 ((~(m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) | m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 2.04/1.56 inference(tautology,[status(thm)],[])).
% 2.04/1.56 tff(239,plain,
% 2.04/1.56 ((~(m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) | m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[238, 237])).
% 2.04/1.56 tff(240,plain,
% 2.04/1.56 (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[239, 108])).
% 2.04/1.56 tff(241,plain,
% 2.04/1.56 (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[240, 65])).
% 2.04/1.56 tff(242,plain,
% 2.04/1.56 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))))))))))))), rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(243,plain,
% 2.04/1.56 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[242])).
% 2.04/1.56 tff(244,plain,
% 2.04/1.56 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(245,plain,
% 2.04/1.56 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[244])).
% 2.04/1.56 tff(246,plain,
% 2.04/1.56 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(247,plain,
% 2.04/1.56 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[246])).
% 2.04/1.56 tff(248,plain,
% 2.04/1.56 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))),
% 2.04/1.56 inference(transitivity,[status(thm)],[247, 245])).
% 2.04/1.56 tff(249,plain,
% 2.04/1.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(250,plain,
% 2.04/1.56 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[249])).
% 2.04/1.56 tff(251,plain,
% 2.04/1.56 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | ((~(~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) & ((r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(252,plain,
% 2.04/1.56 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | ((~(~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) & ((r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))),
% 2.04/1.57 inference(quant_intro,[status(thm)],[251])).
% 2.04/1.57 tff(253,plain,
% 2.04/1.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(254,plain,
% 2.04/1.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))) <=> ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))) <=> (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))), rewrite((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))))), (![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))))),
% 2.04/1.57 inference(bind,[status(th)],[])).
% 2.04/1.57 tff(255,plain,
% 2.04/1.57 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))),
% 2.04/1.57 inference(quant_intro,[status(thm)],[254])).
% 2.04/1.57 tff(256,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k4_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_autgroup')).
% 2.04/1.57 tff(257,plain,
% 2.04/1.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[256, 255])).
% 2.04/1.57 tff(258,plain,
% 2.04/1.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k4_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, D)))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[257, 253])).
% 2.04/1.57 tff(259,plain,(
% 2.04/1.57 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | ((~(~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) & ((r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))))))))),
% 2.04/1.57 inference(skolemize,[status(sab)],[258])).
% 2.04/1.57 tff(260,plain,
% 2.04/1.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (((~r2_hidden(C, B)) | (m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A)))))) & (r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D))))))))) & ((B = k4_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))) & (r2_hidden(tptp_fun_C_3(B, A), B) | (m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))) & ((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[259, 252])).
% 2.04/1.57 tff(261,plain,
% 2.04/1.57 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[260, 250])).
% 2.04/1.57 tff(262,plain,
% 2.04/1.57 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A))))))))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D)))))))))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[261, 248])).
% 2.04/1.57 tff(263,plain,
% 2.04/1.57 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[262, 243])).
% 2.04/1.57 tff(264,plain,
% 2.04/1.57 (v4_group_1(A!0)),
% 2.04/1.57 inference(and_elim,[status(thm)],[22])).
% 2.04/1.57 tff(265,plain,
% 2.04/1.57 (v3_group_1(A!0)),
% 2.04/1.57 inference(and_elim,[status(thm)],[22])).
% 2.04/1.57 tff(266,plain,
% 2.04/1.57 (v1_group_1(A!0)),
% 2.04/1.57 inference(and_elim,[status(thm)],[22])).
% 2.04/1.57 tff(267,plain,
% 2.04/1.57 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(268,plain,
% 2.04/1.57 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(269,plain,
% 2.04/1.57 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))))),
% 2.04/1.57 inference(monotonicity,[status(thm)],[268])).
% 2.04/1.57 tff(270,plain,
% 2.04/1.57 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))),
% 2.04/1.57 inference(transitivity,[status(thm)],[269, 267])).
% 2.04/1.57 tff(271,plain,
% 2.04/1.57 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0)))))))))))))))))),
% 2.04/1.57 inference(quant_inst,[status(thm)],[])).
% 2.04/1.57 tff(272,plain,
% 2.04/1.57 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, E) = k2_group_3(A, E, tptp_fun_D_1(C, A))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_E_2(D, C, A)) = k2_group_3(A, tptp_fun_E_2(D, C, A), D)))))))))))) | (~((B = k4_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), tptp_fun_E_5(D, B, A)) = k2_group_3(A, tptp_fun_E_5(D, B, A), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), tptp_fun_C_3(B, A), E) = k2_group_3(A, E, tptp_fun_D_4(B, A)))))))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[271, 270])).
% 2.04/1.57 tff(273,plain,
% 2.04/1.57 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[272, 41, 266, 265, 264, 23, 263])).
% 2.04/1.57 tff(274,plain,
% 2.04/1.57 (^[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))))),
% 2.04/1.57 inference(bind,[status(th)],[])).
% 2.04/1.57 tff(275,plain,
% 2.04/1.57 (![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)))),
% 2.04/1.57 inference(quant_intro,[status(thm)],[274])).
% 2.04/1.57 tff(276,plain,
% 2.04/1.57 (^[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)))))),
% 2.04/1.57 inference(bind,[status(th)],[])).
% 2.04/1.57 tff(277,plain,
% 2.04/1.57 (![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)))),
% 2.04/1.57 inference(quant_intro,[status(thm)],[276])).
% 2.04/1.57 tff(278,plain,
% 2.04/1.57 (![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)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(279,plain,
% 2.04/1.58 (^[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)))))),
% 2.04/1.58 inference(bind,[status(th)],[])).
% 2.04/1.58 tff(280,plain,
% 2.04/1.58 (![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)))),
% 2.04/1.58 inference(quant_intro,[status(thm)],[279])).
% 2.04/1.58 tff(281,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/sandbox/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 2.04/1.58 tff(282,plain,
% 2.04/1.58 (![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)))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[281, 280])).
% 2.04/1.58 tff(283,plain,
% 2.04/1.58 (![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)))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[282, 278])).
% 2.04/1.58 tff(284,plain,(
% 2.04/1.58 ![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)))),
% 2.04/1.58 inference(skolemize,[status(sab)],[283])).
% 2.04/1.58 tff(285,plain,
% 2.04/1.58 (![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)))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[284, 277])).
% 2.04/1.58 tff(286,plain,
% 2.04/1.58 (![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)))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[285, 275])).
% 2.04/1.58 tff(287,plain,
% 2.04/1.58 (((~![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) | (~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)) | (~v1_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) | (~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)) | (~v1_group_1(A!0)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(288,plain,
% 2.04/1.58 ((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) | (~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)) | (~v1_group_1(A!0)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(289,plain,
% 2.04/1.58 (((~![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) | (~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)) | (~v1_group_1(A!0))))),
% 2.04/1.58 inference(monotonicity,[status(thm)],[288])).
% 2.04/1.58 tff(290,plain,
% 2.04/1.58 (((~![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) | (~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)) | (~v1_group_1(A!0)))),
% 2.04/1.58 inference(transitivity,[status(thm)],[289, 287])).
% 2.04/1.58 tff(291,plain,
% 2.04/1.58 ((~![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)))),
% 2.04/1.58 inference(quant_inst,[status(thm)],[])).
% 2.04/1.58 tff(292,plain,
% 2.04/1.58 ((~![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) | (~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)) | (~v1_group_1(A!0))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[291, 290])).
% 2.04/1.58 tff(293,plain,
% 2.04/1.58 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[292, 41, 266, 265, 264, 23, 286])).
% 2.04/1.58 tff(294,plain,
% 2.04/1.58 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(295,plain,
% 2.04/1.58 (((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(k4_autgroup(A!0) = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((k4_autgroup(A!0) = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k4_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), tptp_fun_E_5(D, k4_autgroup(A!0), A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, k4_autgroup(A!0), A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0)) | (~((~m1_subset_1(tptp_fun_D_4(k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(k4_autgroup(A!0), A!0)))))))))))))))) <=> ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(296,plain,
% 2.04/1.58 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(k4_autgroup(A!0) = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((k4_autgroup(A!0) = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k4_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), tptp_fun_E_5(D, k4_autgroup(A!0), A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, k4_autgroup(A!0), A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0)) | (~((~m1_subset_1(tptp_fun_D_4(k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(k4_autgroup(A!0), A!0))))))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))))),
% 2.04/1.58 inference(monotonicity,[status(thm)],[295])).
% 2.04/1.58 tff(297,plain,
% 2.04/1.58 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(k4_autgroup(A!0) = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((k4_autgroup(A!0) = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k4_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), tptp_fun_E_5(D, k4_autgroup(A!0), A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, k4_autgroup(A!0), A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0)) | (~((~m1_subset_1(tptp_fun_D_4(k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(k4_autgroup(A!0), A!0))))))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))),
% 2.04/1.58 inference(transitivity,[status(thm)],[296, 294])).
% 2.04/1.58 tff(298,plain,
% 2.04/1.58 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(k4_autgroup(A!0) = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((k4_autgroup(A!0) = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k4_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), tptp_fun_E_5(D, k4_autgroup(A!0), A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, k4_autgroup(A!0), A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0)) | (~((~m1_subset_1(tptp_fun_D_4(k4_autgroup(A!0), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(k4_autgroup(A!0), A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(k4_autgroup(A!0), A!0))))))))))))))))),
% 2.04/1.58 inference(quant_inst,[status(thm)],[])).
% 2.04/1.58 tff(299,plain,
% 2.04/1.58 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((~(B = k4_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, B)) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, B) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D)))))))))))) | (~((B = k4_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_5(D, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), tptp_fun_E_5(D, B, A!0)) = k2_group_3(A!0, tptp_fun_E_5(D, B, A!0), D))))))) | (~(r2_hidden(tptp_fun_C_3(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_C_3(B, A!0), E) = k2_group_3(A!0, E, tptp_fun_D_4(B, A!0))))))))))))))))) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[298, 297])).
% 2.04/1.58 tff(300,plain,
% 2.04/1.58 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[299, 293, 273])).
% 2.04/1.58 tff(301,plain,
% 2.04/1.58 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))) | ((~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))) | (~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))))))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(302,plain,
% 2.04/1.59 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))) | ((~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))))))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(303,plain,
% 2.04/1.59 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(C, k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(C, A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, E) = k2_group_3(A!0, E, tptp_fun_D_1(C, A!0))))))))) | (~(r2_hidden(C, k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, C, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_E_2(D, C, A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, C, A!0), D))))))))))) | (~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))))))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[302, 301])).
% 2.04/1.59 tff(304,plain,
% 2.04/1.59 ((~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[303, 300])).
% 2.04/1.59 tff(305,plain,
% 2.04/1.59 (~((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[304, 241])).
% 2.04/1.59 tff(306,plain,
% 2.04/1.59 (((~((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | (~((~m1_subset_1(tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), E) = k2_group_3(A!0, E, tptp_fun_D_1(k6_relat_1(u1_struct_0(A!0)), A!0))))))))) | (~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))))) | (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))),
% 2.04/1.59 inference(tautology,[status(thm)],[])).
% 2.04/1.59 tff(307,plain,
% 2.04/1.59 (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[306, 305])).
% 2.04/1.59 tff(308,plain,
% 2.04/1.59 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(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)) <=> m1_subset_1(D, k4_autgroup(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(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)) <=> m1_subset_1(D, k4_autgroup(A!0))))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(309,plain,
% 2.04/1.59 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(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)) <=> m1_subset_1(D, k4_autgroup(A!0))))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(310,plain,
% 2.04/1.59 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(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)) <=> m1_subset_1(D, k4_autgroup(A!0)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[309, 308])).
% 2.04/1.59 tff(311,plain,
% 2.04/1.59 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[310, 101, 49, 293])).
% 2.04/1.59 tff(312,plain,
% 2.04/1.59 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))) | (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(313,plain,
% 2.04/1.59 (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[312, 311])).
% 2.04/1.59 tff(314,plain,
% 2.04/1.59 (m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(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))),
% 2.04/1.59 inference(monotonicity,[status(thm)],[118])).
% 2.04/1.59 tff(315,plain,
% 2.04/1.59 (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_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 2.04/1.59 inference(symmetry,[status(thm)],[314])).
% 2.04/1.59 tff(316,plain,
% 2.04/1.59 ((~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_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 2.04/1.59 inference(monotonicity,[status(thm)],[315])).
% 2.04/1.59 tff(317,plain,
% 2.04/1.59 (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 2.04/1.59 inference(or_elim,[status(thm)],[21])).
% 2.04/1.59 tff(318,plain,
% 2.04/1.59 (~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[317, 316])).
% 2.04/1.59 tff(319,plain,
% 2.04/1.59 ((~(m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 2.04/1.59 inference(tautology,[status(thm)],[])).
% 2.04/1.59 tff(320,plain,
% 2.04/1.59 (~m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[319, 318, 313])).
% 2.04/1.59 tff(321,plain,
% 2.04/1.59 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(322,plain,
% 2.04/1.59 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(323,plain,
% 2.04/1.59 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[322, 321])).
% 2.04/1.59 tff(324,plain,
% 2.04/1.59 ((~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))) | m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[323, 233])).
% 2.04/1.59 tff(325,plain,
% 2.04/1.59 (~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[324, 320])).
% 2.04/1.59 tff(326,plain,
% 2.04/1.59 ((~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))) | r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))),
% 2.04/1.59 inference(tautology,[status(thm)],[])).
% 2.04/1.59 tff(327,plain,
% 2.04/1.59 ((~(r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D))))))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[326, 325])).
% 2.04/1.59 tff(328,plain,
% 2.04/1.59 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[327, 307])).
% 2.04/1.59 tff(329,plain,
% 2.04/1.59 (^[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))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(330,plain,
% 2.04/1.59 (![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)))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[329])).
% 2.04/1.59 tff(331,plain,
% 2.04/1.59 (^[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)))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(332,plain,
% 2.04/1.59 (![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)))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[331])).
% 2.04/1.59 tff(333,plain,
% 2.04/1.59 (![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)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(334,plain,
% 2.04/1.59 (^[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))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(335,plain,
% 2.04/1.59 (![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)))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[334])).
% 2.04/1.59 tff(336,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/sandbox/benchmark/theBenchmark.p','dt_k2_group_1')).
% 2.04/1.59 tff(337,plain,
% 2.04/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[336, 335])).
% 2.04/1.59 tff(338,plain,
% 2.04/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[337, 333])).
% 2.04/1.59 tff(339,plain,(
% 2.04/1.59 ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 2.04/1.59 inference(skolemize,[status(sab)],[338])).
% 2.04/1.59 tff(340,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[339, 332])).
% 2.04/1.59 tff(341,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[340, 330])).
% 2.04/1.59 tff(342,plain,
% 2.04/1.59 (((~![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)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(343,plain,
% 2.04/1.59 ((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)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(344,plain,
% 2.04/1.59 (((~![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))))),
% 2.04/1.59 inference(monotonicity,[status(thm)],[343])).
% 2.04/1.59 tff(345,plain,
% 2.04/1.59 (((~![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)))),
% 2.04/1.59 inference(transitivity,[status(thm)],[344, 342])).
% 2.04/1.59 tff(346,plain,
% 2.04/1.59 ((~![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)))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(347,plain,
% 2.04/1.59 ((~![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))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[346, 345])).
% 2.04/1.59 tff(348,plain,
% 2.04/1.59 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[347, 41, 23, 341])).
% 2.04/1.59 tff(349,plain,
% 2.04/1.59 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))))))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(350,plain,
% 2.04/1.59 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))))))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(351,plain,
% 2.04/1.59 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(D, k6_relat_1(u1_struct_0(A!0)), A!0), D)))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)))))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[350, 349])).
% 2.04/1.59 tff(352,plain,
% 2.04/1.59 (~((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[351, 348, 328])).
% 2.04/1.59 tff(353,plain,
% 2.04/1.59 (((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)))) | m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))),
% 2.04/1.59 inference(tautology,[status(thm)],[])).
% 2.04/1.59 tff(354,plain,
% 2.04/1.59 (m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[353, 352])).
% 2.04/1.59 tff(355,plain,
% 2.04/1.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(356,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[355])).
% 2.04/1.59 tff(357,plain,
% 2.04/1.59 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(358,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[357])).
% 2.04/1.59 tff(359,plain,
% 2.04/1.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(360,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[359])).
% 2.04/1.59 tff(361,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.59 inference(transitivity,[status(thm)],[360, 358])).
% 2.04/1.59 tff(362,plain,
% 2.04/1.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(363,plain,
% 2.04/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[362])).
% 2.04/1.59 tff(364,plain,
% 2.04/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(365,plain,
% 2.04/1.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))))),
% 2.04/1.59 inference(bind,[status(th)],[])).
% 2.04/1.59 tff(366,plain,
% 2.04/1.59 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(quant_intro,[status(thm)],[365])).
% 2.04/1.59 tff(367,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_group_3')).
% 2.04/1.59 tff(368,plain,
% 2.04/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[367, 366])).
% 2.04/1.59 tff(369,plain,
% 2.04/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[368, 364])).
% 2.04/1.59 tff(370,plain,(
% 2.04/1.59 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(skolemize,[status(sab)],[369])).
% 2.04/1.59 tff(371,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[370, 363])).
% 2.04/1.59 tff(372,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[371, 361])).
% 2.04/1.59 tff(373,plain,
% 2.04/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[372, 356])).
% 2.04/1.59 tff(374,plain,
% 2.04/1.59 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C)))))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(375,plain,
% 2.04/1.59 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C)))))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(376,plain,
% 2.04/1.59 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_group_3(A, B, C) = k1_group_1(A, k1_group_1(A, k3_group_1(A, C), B), C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C))))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[375, 374])).
% 2.04/1.59 tff(377,plain,
% 2.04/1.59 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C))))),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[376, 41, 265, 264, 23, 373])).
% 2.04/1.59 tff(378,plain,
% 2.04/1.59 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C))))) | ((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C))))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(379,plain,
% 2.04/1.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C))))) | ((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C))))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(380,plain,
% 2.04/1.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, B, C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), B), C))))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[379, 378])).
% 2.04/1.60 tff(381,plain,
% 2.04/1.60 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C)))),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[380, 377, 354])).
% 2.04/1.60 tff(382,plain,
% 2.04/1.60 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C)))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(383,plain,
% 2.04/1.60 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C)))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0))))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(384,plain,
% 2.04/1.60 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), C) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, C), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), C)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[383, 382])).
% 2.04/1.60 tff(385,plain,
% 2.04/1.60 (k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0))),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[384, 348, 381])).
% 2.04/1.60 tff(386,plain,
% 2.04/1.60 (k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))),
% 2.04/1.60 inference(symmetry,[status(thm)],[385])).
% 2.04/1.60 tff(387,plain,
% 2.04/1.60 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(388,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[387])).
% 2.04/1.60 tff(389,plain,
% 2.04/1.60 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_group_1(A)) <=> (~(v3_struct_0(A) | (~v2_group_1(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A))) <=> (v3_struct_0(A) | (~v3_group_1(A))))), ((((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A)))) <=> ((~(v3_struct_0(A) | (~v2_group_1(A)))) | (~l1_group_1(A)) | (v3_struct_0(A) | (~v3_group_1(A)))))), rewrite(((~(v3_struct_0(A) | (~v2_group_1(A)))) | (~l1_group_1(A)) | (v3_struct_0(A) | (~v3_group_1(A)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))), ((((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(390,plain,
% 2.04/1.60 (![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[389])).
% 2.04/1.60 tff(391,plain,
% 2.04/1.60 (![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(392,plain,
% 2.04/1.60 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) => ((~v3_struct_0(A)) & v2_group_1(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A))) | ((~v3_struct_0(A)) & v2_group_1(A)))), ((l1_group_1(A) => (((~v3_struct_0(A)) & v3_group_1(A)) => ((~v3_struct_0(A)) & v2_group_1(A)))) <=> (l1_group_1(A) => ((~((~v3_struct_0(A)) & v3_group_1(A))) | ((~v3_struct_0(A)) & v2_group_1(A)))))), rewrite((l1_group_1(A) => ((~((~v3_struct_0(A)) & v3_group_1(A))) | ((~v3_struct_0(A)) & v2_group_1(A)))) <=> (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))), ((l1_group_1(A) => (((~v3_struct_0(A)) & v3_group_1(A)) => ((~v3_struct_0(A)) & v2_group_1(A)))) <=> (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(393,plain,
% 2.04/1.60 (![A: $i] : (l1_group_1(A) => (((~v3_struct_0(A)) & v3_group_1(A)) => ((~v3_struct_0(A)) & v2_group_1(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[392])).
% 2.04/1.60 tff(394,axiom,(![A: $i] : (l1_group_1(A) => (((~v3_struct_0(A)) & v3_group_1(A)) => ((~v3_struct_0(A)) & v2_group_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_group_1')).
% 2.04/1.60 tff(395,plain,
% 2.04/1.60 (![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[394, 393])).
% 2.04/1.60 tff(396,plain,
% 2.04/1.60 (![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[395, 391])).
% 2.04/1.60 tff(397,plain,(
% 2.04/1.60 ![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 2.04/1.60 inference(skolemize,[status(sab)],[396])).
% 2.04/1.60 tff(398,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[397, 390])).
% 2.04/1.60 tff(399,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[398, 388])).
% 2.04/1.60 tff(400,plain,
% 2.04/1.60 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(401,plain,
% 2.04/1.60 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))) | (~v3_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(402,plain,
% 2.04/1.60 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))) | (~v3_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0))))))),
% 2.04/1.60 inference(monotonicity,[status(thm)],[401])).
% 2.04/1.60 tff(403,plain,
% 2.04/1.60 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))) | (~v3_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))))),
% 2.04/1.60 inference(transitivity,[status(thm)],[402, 400])).
% 2.04/1.60 tff(404,plain,
% 2.04/1.60 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))) | (~v3_group_1(A!0)))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(405,plain,
% 2.04/1.60 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~(v3_struct_0(A!0) | (~v2_group_1(A!0))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[404, 403])).
% 2.04/1.60 tff(406,plain,
% 2.04/1.60 (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[405, 41, 265, 23, 399])).
% 2.04/1.60 tff(407,plain,
% 2.04/1.60 ((v3_struct_0(A!0) | (~v2_group_1(A!0))) | v2_group_1(A!0)),
% 2.04/1.60 inference(tautology,[status(thm)],[])).
% 2.04/1.60 tff(408,plain,
% 2.04/1.60 (v2_group_1(A!0)),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[407, 406])).
% 2.04/1.60 tff(409,plain,
% 2.04/1.60 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(410,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[409])).
% 2.04/1.60 tff(411,plain,
% 2.04/1.60 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(412,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[411])).
% 2.04/1.60 tff(413,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))),
% 2.04/1.60 inference(transitivity,[status(thm)],[412, 410])).
% 2.04/1.60 tff(414,plain,
% 2.04/1.60 (^[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))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(415,plain,
% 2.04/1.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[414])).
% 2.04/1.60 tff(416,plain,
% 2.04/1.60 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))) | (~v2_group_1(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A))))))))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(417,plain,
% 2.04/1.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))) | (~v2_group_1(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[416])).
% 2.04/1.60 tff(418,plain,
% 2.04/1.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A)))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(419,plain,
% 2.04/1.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) <=> ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))), ((m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))), ((v2_group_1(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))) <=> (v2_group_1(A) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))))), rewrite((v2_group_1(A) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))) <=> ((~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))), ((v2_group_1(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))) <=> ((~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))))), ((((~v3_struct_0(A)) & l1_group_1(A)) => (v2_group_1(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))) <=> (((~v3_struct_0(A)) & l1_group_1(A)) => ((~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))))), rewrite((((~v3_struct_0(A)) & l1_group_1(A)) => ((~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A)))), ((((~v3_struct_0(A)) & l1_group_1(A)) => (v2_group_1(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A)))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(420,plain,
% 2.04/1.60 (![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => (v2_group_1(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A)))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[419])).
% 2.04/1.60 tff(421,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => (v2_group_1(A) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((B = k2_group_1(A)) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_group_1')).
% 2.04/1.60 tff(422,plain,
% 2.04/1.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[421, 420])).
% 2.04/1.60 tff(423,plain,
% 2.04/1.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((B = k2_group_1(A)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C))))) | (~v2_group_1(A)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[422, 418])).
% 2.04/1.60 tff(424,plain,(
% 2.04/1.60 ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))) | (~v2_group_1(A)))),
% 2.04/1.60 inference(skolemize,[status(sab)],[423])).
% 2.04/1.60 tff(425,plain,
% 2.04/1.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k1_group_1(A, C, B) = C) & (k1_group_1(A, B, C) = C)))) & ((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | ((k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A)) & (k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[424, 417])).
% 2.04/1.60 tff(426,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[425, 415])).
% 2.04/1.60 tff(427,plain,
% 2.04/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[426, 413])).
% 2.04/1.60 tff(428,plain,
% 2.04/1.60 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v2_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v2_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0)))))))))))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(429,plain,
% 2.04/1.60 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v2_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0)))))))))))))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(430,plain,
% 2.04/1.60 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v2_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~((~(B = k2_group_1(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k1_group_1(A, C, B) = C)) | (~(k1_group_1(A, B, C) = C))))))) | (~((B = k2_group_1(A)) | (~((~m1_subset_1(tptp_fun_C_6(B, A), u1_struct_0(A))) | (~((~(k1_group_1(A, tptp_fun_C_6(B, A), B) = tptp_fun_C_6(B, A))) | (~(k1_group_1(A, B, tptp_fun_C_6(B, A)) = tptp_fun_C_6(B, A)))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v2_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[429, 428])).
% 2.04/1.60 tff(431,plain,
% 2.04/1.60 ((~v2_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[430, 41, 23, 427])).
% 2.04/1.60 tff(432,plain,
% 2.04/1.60 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[431, 408])).
% 2.04/1.60 tff(433,plain,
% 2.04/1.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(434,plain,
% 2.04/1.60 (((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~((~(k2_group_1(A!0) = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))) | (~((k2_group_1(A!0) = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(k2_group_1(A!0), A!0), k2_group_1(A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_C_6(k2_group_1(A!0), A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0)))))))))))) <=> ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(435,plain,
% 2.04/1.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~((~(k2_group_1(A!0) = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))) | (~((k2_group_1(A!0) = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(k2_group_1(A!0), A!0), k2_group_1(A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_C_6(k2_group_1(A!0), A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))))),
% 2.04/1.60 inference(monotonicity,[status(thm)],[434])).
% 2.04/1.60 tff(436,plain,
% 2.04/1.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~((~(k2_group_1(A!0) = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))) | (~((k2_group_1(A!0) = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(k2_group_1(A!0), A!0), k2_group_1(A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_C_6(k2_group_1(A!0), A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))),
% 2.04/1.60 inference(transitivity,[status(thm)],[435, 433])).
% 2.04/1.60 tff(437,plain,
% 2.04/1.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~((~((~(k2_group_1(A!0) = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C))))))) | (~((k2_group_1(A!0) = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(k2_group_1(A!0), A!0), k2_group_1(A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_C_6(k2_group_1(A!0), A!0)) = tptp_fun_C_6(k2_group_1(A!0), A!0))))))))))))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(438,plain,
% 2.04/1.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~((~(B = k2_group_1(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, B) = C)) | (~(k1_group_1(A!0, B, C) = C))))))) | (~((B = k2_group_1(A!0)) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_C_6(B, A!0), B) = tptp_fun_C_6(B, A!0))) | (~(k1_group_1(A!0, B, tptp_fun_C_6(B, A!0)) = tptp_fun_C_6(B, A!0))))))))))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[437, 436])).
% 2.04/1.60 tff(439,plain,
% 2.04/1.60 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[438, 348, 432])).
% 2.04/1.60 tff(440,plain,
% 2.04/1.60 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))) | ((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(441,plain,
% 2.04/1.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))) | ((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(442,plain,
% 2.04/1.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, C, k2_group_1(A!0)) = C)) | (~(k1_group_1(A!0, k2_group_1(A!0), C) = C)))))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (~((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[441, 440])).
% 2.04/1.61 tff(443,plain,
% 2.04/1.61 (~((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[442, 439, 354])).
% 2.04/1.61 tff(444,plain,
% 2.04/1.61 (((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))) | (k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))),
% 2.04/1.61 inference(tautology,[status(thm)],[])).
% 2.04/1.61 tff(445,plain,
% 2.04/1.61 (k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[444, 443])).
% 2.04/1.61 tff(446,plain,
% 2.04/1.61 (^[A: $i] : refl((v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(447,plain,
% 2.04/1.61 (![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[446])).
% 2.04/1.61 tff(448,plain,
% 2.04/1.61 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(449,plain,
% 2.04/1.61 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[448])).
% 2.04/1.61 tff(450,plain,
% 2.04/1.61 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(451,plain,
% 2.04/1.61 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(452,plain,
% 2.04/1.61 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k3_group_1(A, k2_group_1(A)) = k2_group_1(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[451])).
% 2.04/1.61 tff(453,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_group_1')).
% 2.04/1.61 tff(454,plain,
% 2.04/1.61 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[453, 452])).
% 2.04/1.61 tff(455,plain,
% 2.04/1.61 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[454, 450])).
% 2.04/1.61 tff(456,plain,(
% 2.04/1.61 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)))),
% 2.04/1.61 inference(skolemize,[status(sab)],[455])).
% 2.04/1.61 tff(457,plain,
% 2.04/1.61 (![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[456, 449])).
% 2.04/1.61 tff(458,plain,
% 2.04/1.61 (![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[457, 447])).
% 2.04/1.61 tff(459,plain,
% 2.04/1.61 (((~![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(460,plain,
% 2.04/1.61 ((v3_struct_0(A!0) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(461,plain,
% 2.04/1.61 (((~![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_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) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0))))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[460])).
% 2.04/1.61 tff(462,plain,
% 2.04/1.61 (((~![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_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) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)))),
% 2.04/1.61 inference(transitivity,[status(thm)],[461, 459])).
% 2.04/1.61 tff(463,plain,
% 2.04/1.61 ((~![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(464,plain,
% 2.04/1.61 ((~![A: $i] : (v3_struct_0(A) | (k3_group_1(A, k2_group_1(A)) = k2_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[463, 462])).
% 2.04/1.61 tff(465,plain,
% 2.04/1.61 (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[464, 41, 265, 264, 23, 458])).
% 2.04/1.61 tff(466,plain,
% 2.04/1.61 (k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[465])).
% 2.04/1.61 tff(467,plain,
% 2.04/1.61 (k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)),
% 2.04/1.61 inference(transitivity,[status(thm)],[466, 445])).
% 2.04/1.61 tff(468,plain,
% 2.04/1.61 (k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0)) = k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[467])).
% 2.04/1.61 tff(469,plain,
% 2.04/1.61 (k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = k1_group_1(A!0, k1_group_1(A!0, k3_group_1(A!0, k2_group_1(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)), k2_group_1(A!0))),
% 2.04/1.61 inference(symmetry,[status(thm)],[468])).
% 2.04/1.61 tff(470,plain,
% 2.04/1.61 (((~(k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~(k1_group_1(A!0, k2_group_1(A!0), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))) | (k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))),
% 2.04/1.61 inference(tautology,[status(thm)],[])).
% 2.04/1.61 tff(471,plain,
% 2.04/1.61 (k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[470, 443])).
% 2.04/1.61 tff(472,plain,
% 2.04/1.61 (tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0) = k1_group_1(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))),
% 2.04/1.61 inference(symmetry,[status(thm)],[471])).
% 2.04/1.61 tff(473,plain,
% 2.04/1.61 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(474,plain,
% 2.04/1.61 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[473])).
% 2.04/1.61 tff(475,plain,
% 2.04/1.61 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(476,plain,
% 2.04/1.61 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(477,plain,
% 2.04/1.61 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[476])).
% 2.04/1.61 tff(478,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 2.04/1.61 tff(479,plain,
% 2.04/1.61 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[478, 477])).
% 2.04/1.61 tff(480,plain,
% 2.04/1.61 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[479, 475])).
% 2.04/1.61 tff(481,plain,(
% 2.04/1.61 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(skolemize,[status(sab)],[480])).
% 2.04/1.61 tff(482,plain,
% 2.04/1.61 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[481, 474])).
% 2.04/1.61 tff(483,plain,
% 2.04/1.61 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(484,plain,
% 2.04/1.61 ((r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(485,plain,
% 2.04/1.61 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[484])).
% 2.04/1.61 tff(486,plain,
% 2.04/1.61 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)))),
% 2.04/1.61 inference(transitivity,[status(thm)],[485, 483])).
% 2.04/1.61 tff(487,plain,
% 2.04/1.61 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(488,plain,
% 2.04/1.61 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[487, 486])).
% 2.04/1.61 tff(489,plain,
% 2.04/1.61 (r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[488, 482, 49, 354])).
% 2.04/1.61 tff(490,plain,
% 2.04/1.61 (^[A: $i, B: $i] : refl(((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B)) <=> ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B)))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(491,plain,
% 2.04/1.61 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B)) <=> ![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[490])).
% 2.04/1.61 tff(492,plain,
% 2.04/1.61 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B)) <=> ![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(493,plain,
% 2.04/1.61 (^[A: $i, B: $i] : rewrite((r2_hidden(B, A) => (k1_funct_1(k6_relat_1(A), B) = B)) <=> ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B)))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(494,plain,
% 2.04/1.61 (![A: $i, B: $i] : (r2_hidden(B, A) => (k1_funct_1(k6_relat_1(A), B) = B)) <=> ![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[493])).
% 2.04/1.61 tff(495,axiom,(![A: $i, B: $i] : (r2_hidden(B, A) => (k1_funct_1(k6_relat_1(A), B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t35_funct_1')).
% 2.04/1.61 tff(496,plain,
% 2.04/1.61 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[495, 494])).
% 2.04/1.61 tff(497,plain,
% 2.04/1.61 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[496, 492])).
% 2.04/1.61 tff(498,plain,(
% 2.04/1.61 ![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(skolemize,[status(sab)],[497])).
% 2.04/1.61 tff(499,plain,
% 2.04/1.61 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[498, 491])).
% 2.04/1.61 tff(500,plain,
% 2.04/1.61 (((~![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))) | ((~r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))) | (~r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(501,plain,
% 2.04/1.61 ((~![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))) | ((~r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(502,plain,
% 2.04/1.61 ((~![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))) | (~r2_hidden(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[501, 500])).
% 2.04/1.61 tff(503,plain,
% 2.04/1.61 (k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[502, 499, 489])).
% 2.04/1.61 tff(504,plain,
% 2.04/1.61 (^[A: $i, B: $i, C: $i, D: $i] : refl((v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(505,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[504])).
% 2.04/1.61 tff(506,plain,
% 2.04/1.61 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(507,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[506])).
% 2.04/1.61 tff(508,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(509,plain,
% 2.04/1.61 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(510,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[509])).
% 2.04/1.61 tff(511,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 2.04/1.61 tff(512,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[511, 510])).
% 2.04/1.61 tff(513,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[512, 508])).
% 2.04/1.61 tff(514,plain,(
% 2.04/1.61 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.04/1.61 inference(skolemize,[status(sab)],[513])).
% 2.04/1.61 tff(515,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[514, 507])).
% 2.04/1.61 tff(516,plain,
% 2.04/1.61 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[515, 505])).
% 2.04/1.61 tff(517,plain,
% 2.04/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(518,plain,
% 2.04/1.61 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(519,plain,
% 2.04/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[518])).
% 2.04/1.61 tff(520,plain,
% 2.04/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))))),
% 2.04/1.61 inference(transitivity,[status(thm)],[519, 517])).
% 2.04/1.61 tff(521,plain,
% 2.04/1.61 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(522,plain,
% 2.04/1.61 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[521, 520])).
% 2.04/1.61 tff(523,plain,
% 2.04/1.61 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k1_funct_1(k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0))),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[522, 516, 49, 157, 196, 173, 354])).
% 2.04/1.61 tff(524,plain,
% 2.04/1.61 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))),
% 2.04/1.61 inference(transitivity,[status(thm)],[523, 503, 472, 469, 386])).
% 2.04/1.61 tff(525,plain,
% 2.04/1.61 (((~m1_subset_1(tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)))) | (~(k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0))))),
% 2.04/1.62 inference(tautology,[status(thm)],[])).
% 2.04/1.62 tff(526,plain,
% 2.04/1.62 (~(k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_relat_1(u1_struct_0(A!0)), tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0)) = k2_group_3(A!0, tptp_fun_E_2(k2_group_1(A!0), k6_relat_1(u1_struct_0(A!0)), A!0), k2_group_1(A!0)))),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[525, 352])).
% 2.04/1.62 tff(527,plain,
% 2.04/1.62 ($false),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[526, 524])).
% 2.04/1.62 % SZS output end Proof
%------------------------------------------------------------------------------