%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP625+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:08:12 AM UTC 2025
% Result : Theorem 1.48s 1.67s
% Output : Proof 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP625+1 : TPTP v9.0.0. Released v3.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:27:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.48/1.67 % SZS status Theorem
% 1.48/1.67 % SZS output start Proof
% 1.48/1.67 tff(k2_group_3_type, type, (
% 1.48/1.67 k2_group_3: ( $i * $i * $i ) > $i)).
% 1.48/1.67 tff(k2_group_1_type, type, (
% 1.48/1.67 k2_group_1: $i > $i)).
% 1.48/1.67 tff(tptp_fun_A_0_type, type, (
% 1.48/1.67 tptp_fun_A_0: $i)).
% 1.48/1.67 tff(tptp_fun_E_2_type, type, (
% 1.48/1.67 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 1.48/1.67 tff(k6_relat_1_type, type, (
% 1.48/1.67 k6_relat_1: $i > $i)).
% 1.48/1.67 tff(u1_struct_0_type, type, (
% 1.48/1.67 u1_struct_0: $i > $i)).
% 1.48/1.67 tff(k8_funct_2_type, type, (
% 1.48/1.67 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 1.48/1.67 tff(k1_group_1_type, type, (
% 1.48/1.67 k1_group_1: ( $i * $i * $i ) > $i)).
% 1.48/1.67 tff(k3_group_1_type, type, (
% 1.48/1.67 k3_group_1: ( $i * $i ) > $i)).
% 1.48/1.67 tff(m1_subset_1_type, type, (
% 1.48/1.67 m1_subset_1: ( $i * $i ) > $o)).
% 1.48/1.67 tff(r2_hidden_type, type, (
% 1.48/1.67 r2_hidden: ( $i * $i ) > $o)).
% 1.48/1.67 tff(k4_autgroup_type, type, (
% 1.48/1.67 k4_autgroup: $i > $i)).
% 1.48/1.67 tff(tptp_fun_D_1_type, type, (
% 1.48/1.67 tptp_fun_D_1: ( $i * $i ) > $i)).
% 1.48/1.67 tff(m2_fraenkel_type, type, (
% 1.48/1.67 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 1.48/1.67 tff(k1_fraenkel_type, type, (
% 1.48/1.67 k1_fraenkel: ( $i * $i ) > $i)).
% 1.48/1.67 tff(k1_funct_2_type, type, (
% 1.48/1.67 k1_funct_2: ( $i * $i ) > $i)).
% 1.48/1.67 tff(v1_xboole_0_type, type, (
% 1.48/1.67 v1_xboole_0: $i > $o)).
% 1.48/1.67 tff(l1_struct_0_type, type, (
% 1.48/1.67 l1_struct_0: $i > $o)).
% 1.48/1.67 tff(l1_group_1_type, type, (
% 1.48/1.67 l1_group_1: $i > $o)).
% 1.48/1.67 tff(v4_group_1_type, type, (
% 1.48/1.67 v4_group_1: $i > $o)).
% 1.48/1.67 tff(v3_group_1_type, type, (
% 1.48/1.67 v3_group_1: $i > $o)).
% 1.48/1.67 tff(v1_group_1_type, type, (
% 1.48/1.67 v1_group_1: $i > $o)).
% 1.48/1.67 tff(v3_struct_0_type, type, (
% 1.48/1.67 v3_struct_0: $i > $o)).
% 1.48/1.67 tff(k6_partfun1_type, type, (
% 1.48/1.67 k6_partfun1: $i > $i)).
% 1.48/1.67 tff(m1_fraenkel_type, type, (
% 1.48/1.67 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 1.48/1.67 tff(m2_relset_1_type, type, (
% 1.48/1.67 m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.48/1.67 tff(v1_partfun1_type, type, (
% 1.48/1.67 v1_partfun1: ( $i * $i * $i ) > $o)).
% 1.48/1.67 tff(v1_funct_1_type, type, (
% 1.48/1.67 v1_funct_1: $i > $o)).
% 1.48/1.67 tff(v8_relat_2_type, type, (
% 1.48/1.67 v8_relat_2: $i > $o)).
% 1.48/1.67 tff(v4_relat_2_type, type, (
% 1.48/1.67 v4_relat_2: $i > $o)).
% 1.48/1.67 tff(v3_relat_2_type, type, (
% 1.48/1.67 v3_relat_2: $i > $o)).
% 1.48/1.67 tff(v1_relat_1_type, type, (
% 1.48/1.67 v1_relat_1: $i > $o)).
% 1.48/1.67 tff(v1_relat_2_type, type, (
% 1.48/1.67 v1_relat_2: $i > $o)).
% 1.48/1.67 tff(v1_funct_2_type, type, (
% 1.48/1.67 v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.48/1.67 tff(m1_relset_1_type, type, (
% 1.48/1.67 m1_relset_1: ( $i * $i * $i ) > $o)).
% 1.48/1.67 tff(k1_xboole_0_type, type, (
% 1.48/1.67 k1_xboole_0: $i)).
% 1.48/1.67 tff(tptp_fun_C_3_type, type, (
% 1.48/1.67 tptp_fun_C_3: ( $i * $i ) > $i)).
% 1.48/1.67 tff(tptp_fun_D_4_type, type, (
% 1.48/1.67 tptp_fun_D_4: ( $i * $i ) > $i)).
% 1.48/1.67 tff(tptp_fun_E_5_type, type, (
% 1.48/1.67 tptp_fun_E_5: ( $i * $i * $i ) > $i)).
% 1.48/1.67 tff(tptp_fun_C_6_type, type, (
% 1.48/1.67 tptp_fun_C_6: ( $i * $i ) > $i)).
% 1.48/1.67 tff(v2_group_1_type, type, (
% 1.48/1.67 v2_group_1: $i > $o)).
% 1.48/1.67 tff(k1_funct_1_type, type, (
% 1.48/1.67 k1_funct_1: ( $i * $i ) > $i)).
% 1.48/1.67 tff(1,plain,
% 1.48/1.67 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(2,plain,
% 1.48/1.67 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[1])).
% 1.48/1.67 tff(3,plain,
% 1.48/1.67 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(4,plain,
% 1.48/1.67 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(5,plain,
% 1.48/1.67 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[4])).
% 1.48/1.67 tff(6,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 1.48/1.67 tff(7,plain,
% 1.48/1.67 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.48/1.67 tff(8,plain,
% 1.48/1.67 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.48/1.67 tff(9,plain,(
% 1.48/1.67 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(skolemize,[status(sab)],[8])).
% 1.48/1.67 tff(10,plain,
% 1.48/1.67 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.48/1.67 tff(11,plain,
% 1.48/1.67 ((~![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))))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(12,plain,
% 1.48/1.67 ((~![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))))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 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/sandbox2/benchmark/theBenchmark.p','t16_autgroup')).
% 1.48/1.67 tff(14,plain,
% 1.48/1.67 (~![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)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.48/1.67 tff(15,plain,
% 1.48/1.67 (~![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)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[14, 11])).
% 1.48/1.67 tff(16,plain,
% 1.48/1.67 (~![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)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.48/1.67 tff(17,plain,
% 1.48/1.67 (~![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)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[16, 11])).
% 1.48/1.67 tff(18,plain,(
% 1.48/1.67 ~((~((~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)))),
% 1.48/1.67 inference(skolemize,[status(sab)],[17])).
% 1.48/1.67 tff(19,plain,
% 1.48/1.67 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)),
% 1.48/1.67 inference(or_elim,[status(thm)],[18])).
% 1.48/1.67 tff(20,plain,
% 1.48/1.67 (l1_group_1(A!0)),
% 1.48/1.67 inference(and_elim,[status(thm)],[19])).
% 1.48/1.67 tff(21,plain,
% 1.48/1.67 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(22,plain,
% 1.48/1.67 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(23,plain,
% 1.48/1.67 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.48/1.67 tff(24,plain,
% 1.48/1.67 (l1_struct_0(A!0)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 1.48/1.67 tff(25,plain,
% 1.48/1.67 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(26,plain,
% 1.48/1.67 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[25])).
% 1.48/1.67 tff(27,plain,
% 1.48/1.67 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(28,plain,
% 1.48/1.67 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[27])).
% 1.48/1.67 tff(29,plain,
% 1.48/1.67 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(30,plain,
% 1.48/1.67 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(31,plain,
% 1.48/1.67 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[30])).
% 1.48/1.67 tff(32,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 1.48/1.67 tff(33,plain,
% 1.48/1.67 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.48/1.67 tff(34,plain,
% 1.48/1.67 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.48/1.67 tff(35,plain,(
% 1.48/1.67 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.48/1.67 inference(skolemize,[status(sab)],[34])).
% 1.48/1.67 tff(36,plain,
% 1.48/1.67 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[35, 28])).
% 1.48/1.67 tff(37,plain,
% 1.48/1.67 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[36, 26])).
% 1.48/1.67 tff(38,plain,
% 1.48/1.67 (~v3_struct_0(A!0)),
% 1.48/1.67 inference(and_elim,[status(thm)],[19])).
% 1.48/1.67 tff(39,plain,
% 1.48/1.67 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(40,plain,
% 1.48/1.67 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(41,plain,
% 1.48/1.67 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[40])).
% 1.48/1.67 tff(42,plain,
% 1.48/1.67 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.48/1.67 inference(transitivity,[status(thm)],[41, 39])).
% 1.48/1.68 tff(43,plain,
% 1.48/1.68 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(44,plain,
% 1.48/1.68 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.48/1.68 tff(45,plain,
% 1.48/1.68 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[44, 38, 37])).
% 1.48/1.68 tff(46,plain,
% 1.48/1.68 (~v1_xboole_0(u1_struct_0(A!0))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[45, 24])).
% 1.48/1.68 tff(47,plain,
% 1.48/1.68 (^[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))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(48,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[47])).
% 1.48/1.68 tff(49,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(50,plain,
% 1.48/1.68 (^[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))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(51,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[50])).
% 1.48/1.68 tff(52,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_fraenkel')).
% 1.48/1.68 tff(53,plain,
% 1.48/1.68 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.48/1.68 tff(54,plain,
% 1.48/1.68 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.48/1.68 tff(55,plain,(
% 1.48/1.68 ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[54])).
% 1.48/1.68 tff(56,plain,
% 1.48/1.68 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.48/1.68 tff(57,plain,
% 1.48/1.68 (((~![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))))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(58,plain,
% 1.48/1.68 ((~![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))))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(59,plain,
% 1.48/1.68 ((~![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.48/1.68 tff(60,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[59, 56, 46])).
% 1.48/1.68 tff(61,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(symmetry,[status(thm)],[60])).
% 1.48/1.68 tff(62,plain,
% 1.48/1.68 (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)))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[61])).
% 1.48/1.68 tff(63,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[61])).
% 1.48/1.68 tff(64,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(symmetry,[status(thm)],[63])).
% 1.48/1.68 tff(65,plain,
% 1.48/1.68 (^[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)))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(66,plain,
% 1.48/1.68 (![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))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[65])).
% 1.48/1.68 tff(67,plain,
% 1.48/1.68 (![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))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(68,plain,
% 1.48/1.68 (^[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)))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(69,plain,
% 1.48/1.68 (![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))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[68])).
% 1.48/1.68 tff(70,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(B)) => m1_fraenkel(k1_fraenkel(A, B), A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_fraenkel')).
% 1.48/1.68 tff(71,plain,
% 1.48/1.68 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.48/1.68 tff(72,plain,
% 1.48/1.68 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.48/1.68 tff(73,plain,(
% 1.48/1.68 ![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 1.48/1.68 inference(skolemize,[status(sab)],[72])).
% 1.48/1.68 tff(74,plain,
% 1.48/1.68 (![A: $i, B: $i] : (v1_xboole_0(B) | m1_fraenkel(k1_fraenkel(A, B), A, B))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.48/1.68 tff(75,plain,
% 1.48/1.68 (((~![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)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(76,plain,
% 1.48/1.68 ((~![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)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(77,plain,
% 1.48/1.68 ((~![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))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.48/1.68 tff(78,plain,
% 1.48/1.68 (m1_fraenkel(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[77, 74, 46])).
% 1.48/1.68 tff(79,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[78, 64])).
% 1.48/1.68 tff(80,plain,
% 1.48/1.68 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(81,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[80])).
% 1.48/1.68 tff(82,plain,
% 1.48/1.68 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(83,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[82])).
% 1.48/1.68 tff(84,plain,
% 1.48/1.68 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(85,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[84])).
% 1.48/1.68 tff(86,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[85, 83])).
% 1.48/1.68 tff(87,plain,
% 1.48/1.68 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(88,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[87])).
% 1.48/1.68 tff(89,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(90,plain,
% 1.48/1.68 (^[A: $i, B: $i, C: $i] : rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(91,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[90])).
% 1.48/1.68 tff(92,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 1.48/1.68 tff(93,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.48/1.68 tff(94,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[93, 89])).
% 1.48/1.68 tff(95,plain,(
% 1.48/1.68 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[94])).
% 1.48/1.68 tff(96,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[95, 88])).
% 1.48/1.68 tff(97,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[96, 86])).
% 1.48/1.68 tff(98,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[97, 81])).
% 1.48/1.68 tff(99,plain,
% 1.48/1.68 (((~![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)))))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(100,plain,
% 1.48/1.68 ((~![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)))))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(101,plain,
% 1.48/1.68 ((~![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))))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.48/1.68 tff(102,plain,
% 1.48/1.68 ((~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))))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[101, 98, 46])).
% 1.48/1.68 tff(103,plain,
% 1.48/1.68 (![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))))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[102, 79])).
% 1.48/1.68 tff(104,plain,
% 1.48/1.68 ((~![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))))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(105,plain,
% 1.48/1.68 (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)))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[104, 103])).
% 1.48/1.68 tff(106,plain,
% 1.48/1.68 (^[A: $i] : refl((k6_partfun1(A) = k6_relat_1(A)) <=> (k6_partfun1(A) = k6_relat_1(A)))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(107,plain,
% 1.48/1.68 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[106])).
% 1.48/1.68 tff(108,plain,
% 1.48/1.68 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(109,axiom,(![A: $i] : (k6_partfun1(A) = k6_relat_1(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 1.48/1.68 tff(110,plain,
% 1.48/1.68 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.48/1.68 tff(111,plain,(
% 1.48/1.68 ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 1.48/1.68 inference(skolemize,[status(sab)],[110])).
% 1.48/1.68 tff(112,plain,
% 1.48/1.68 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.48/1.68 tff(113,plain,
% 1.48/1.68 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(114,plain,
% 1.48/1.68 (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[113, 112])).
% 1.48/1.68 tff(115,plain,
% 1.48/1.68 (k6_relat_1(u1_struct_0(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 1.48/1.68 inference(symmetry,[status(thm)],[114])).
% 1.48/1.68 tff(116,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[115])).
% 1.48/1.68 tff(117,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(symmetry,[status(thm)],[116])).
% 1.48/1.68 tff(118,plain,
% 1.48/1.68 (^[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)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(119,plain,
% 1.48/1.68 (![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))))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[118])).
% 1.48/1.68 tff(120,plain,
% 1.48/1.68 (^[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)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(121,plain,
% 1.48/1.68 (![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))))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[120])).
% 1.48/1.68 tff(122,plain,
% 1.48/1.68 (![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))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(123,axiom,(![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 1.48/1.68 tff(124,plain,
% 1.48/1.68 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.48/1.68 tff(125,plain,(
% 1.48/1.68 ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 1.48/1.68 inference(skolemize,[status(sab)],[124])).
% 1.48/1.68 tff(126,plain,
% 1.48/1.68 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[125, 121])).
% 1.48/1.68 tff(127,plain,
% 1.48/1.68 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[126, 119])).
% 1.48/1.68 tff(128,plain,
% 1.48/1.68 ((~![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)))))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(129,plain,
% 1.48/1.68 (~((~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))))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[128, 127])).
% 1.48/1.68 tff(130,plain,
% 1.48/1.68 (((~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))),
% 1.48/1.68 inference(tautology,[status(thm)],[])).
% 1.48/1.68 tff(131,plain,
% 1.48/1.68 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.48/1.68 tff(132,plain,
% 1.48/1.68 (m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[131, 117])).
% 1.48/1.68 tff(133,plain,
% 1.48/1.68 (^[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))))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(134,plain,
% 1.48/1.68 (![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)))))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[133])).
% 1.48/1.68 tff(135,plain,
% 1.48/1.68 (^[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))))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(136,plain,
% 1.48/1.68 (![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)))))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[135])).
% 1.48/1.68 tff(137,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(138,plain,
% 1.48/1.68 (^[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)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(139,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[138])).
% 1.48/1.68 tff(140,axiom,(![A: $i] : (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_partfun1')).
% 1.48/1.68 tff(141,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.48/1.68 tff(142,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.48/1.68 tff(143,plain,(
% 1.48/1.68 ![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)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[142])).
% 1.48/1.68 tff(144,plain,
% 1.48/1.68 (![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)))))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[143, 136])).
% 1.48/1.68 tff(145,plain,
% 1.48/1.68 (![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)))))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[144, 134])).
% 1.48/1.68 tff(146,plain,
% 1.48/1.68 (((~![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)))))))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(147,plain,
% 1.48/1.68 ((~((~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))))))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(148,plain,
% 1.48/1.68 (((~![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)))))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[147])).
% 1.48/1.68 tff(149,plain,
% 1.48/1.68 (((~![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)))))))),
% 1.48/1.68 inference(transitivity,[status(thm)],[148, 146])).
% 1.48/1.68 tff(150,plain,
% 1.48/1.68 ((~![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))))))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(151,plain,
% 1.48/1.68 ((~![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))))))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.48/1.68 tff(152,plain,
% 1.48/1.68 (~((~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)))))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[151, 145])).
% 1.48/1.68 tff(153,plain,
% 1.48/1.68 (((~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)))),
% 1.48/1.68 inference(tautology,[status(thm)],[])).
% 1.48/1.68 tff(154,plain,
% 1.48/1.68 (v1_funct_1(k6_relat_1(u1_struct_0(A!0)))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[153, 152])).
% 1.48/1.68 tff(155,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[115])).
% 1.48/1.68 tff(156,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(symmetry,[status(thm)],[155])).
% 1.48/1.68 tff(157,plain,
% 1.48/1.68 (((~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))),
% 1.48/1.68 inference(tautology,[status(thm)],[])).
% 1.48/1.68 tff(158,plain,
% 1.48/1.68 (v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[157, 129])).
% 1.48/1.68 tff(159,plain,
% 1.48/1.68 (v1_partfun1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[158, 156])).
% 1.48/1.68 tff(160,plain,
% 1.48/1.68 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(161,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[160])).
% 1.48/1.68 tff(162,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(163,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 1.48/1.68 tff(164,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.48/1.68 tff(165,plain,(
% 1.48/1.68 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.48/1.68 inference(skolemize,[status(sab)],[164])).
% 1.48/1.68 tff(166,plain,
% 1.48/1.68 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[165, 161])).
% 1.48/1.68 tff(167,plain,
% 1.48/1.68 ((~![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)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(168,plain,
% 1.48/1.68 (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))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.48/1.68 tff(169,plain,
% 1.48/1.68 ((~(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))),
% 1.48/1.68 inference(tautology,[status(thm)],[])).
% 1.48/1.68 tff(170,plain,
% 1.48/1.68 (m1_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[169, 132, 168])).
% 1.48/1.68 tff(171,plain,
% 1.48/1.68 (^[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))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(172,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[171])).
% 1.48/1.68 tff(173,plain,
% 1.48/1.68 (^[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)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(174,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[173])).
% 1.48/1.68 tff(175,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(176,plain,
% 1.48/1.68 (^[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)))))),
% 1.48/1.68 inference(bind,[status(th)],[])).
% 1.48/1.68 tff(177,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(quant_intro,[status(thm)],[176])).
% 1.48/1.68 tff(178,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/sandbox2/benchmark/theBenchmark.p','cc1_funct_2')).
% 1.48/1.68 tff(179,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.48/1.68 tff(180,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[179, 175])).
% 1.48/1.68 tff(181,plain,(
% 1.48/1.68 ![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)))),
% 1.48/1.68 inference(skolemize,[status(sab)],[180])).
% 1.48/1.68 tff(182,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[181, 174])).
% 1.48/1.68 tff(183,plain,
% 1.48/1.68 (![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)))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[182, 172])).
% 1.48/1.68 tff(184,plain,
% 1.48/1.68 (((~![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))))))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(185,plain,
% 1.48/1.69 (((~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))))))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(186,plain,
% 1.48/1.69 (((~![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)))))))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[185])).
% 1.48/1.69 tff(187,plain,
% 1.48/1.69 (((~![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))))))),
% 1.48/1.69 inference(transitivity,[status(thm)],[186, 184])).
% 1.48/1.69 tff(188,plain,
% 1.48/1.69 ((~![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))))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(189,plain,
% 1.48/1.69 ((~![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)))))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.48/1.69 tff(190,plain,
% 1.48/1.69 ((~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)))))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[189, 183])).
% 1.48/1.69 tff(191,plain,
% 1.48/1.69 (~((~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))))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[190, 170, 154, 159])).
% 1.48/1.69 tff(192,plain,
% 1.48/1.69 (((~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))),
% 1.48/1.69 inference(tautology,[status(thm)],[])).
% 1.48/1.69 tff(193,plain,
% 1.48/1.69 (v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[192, 191])).
% 1.48/1.69 tff(194,plain,
% 1.48/1.69 (^[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))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(195,plain,
% 1.48/1.69 (![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)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[194])).
% 1.48/1.69 tff(196,plain,
% 1.48/1.69 (^[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)))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(197,plain,
% 1.48/1.69 (![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)))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[196])).
% 1.48/1.69 tff(198,plain,
% 1.48/1.69 (![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))))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(199,plain,
% 1.48/1.69 (^[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))))))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(200,plain,
% 1.48/1.69 (![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))))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[199])).
% 1.48/1.69 tff(201,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/sandbox2/benchmark/theBenchmark.p','t11_funct_2')).
% 1.48/1.69 tff(202,plain,
% 1.48/1.69 (![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))))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.48/1.69 tff(203,plain,
% 1.48/1.69 (![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))))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.48/1.69 tff(204,plain,(
% 1.48/1.69 ![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))))),
% 1.48/1.69 inference(skolemize,[status(sab)],[203])).
% 1.48/1.69 tff(205,plain,
% 1.48/1.69 (![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)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[204, 197])).
% 1.48/1.69 tff(206,plain,
% 1.48/1.69 (![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)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[205, 195])).
% 1.48/1.69 tff(207,plain,
% 1.48/1.69 (((~![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))))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(208,plain,
% 1.48/1.69 ((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))) | $false | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(209,plain,
% 1.48/1.69 ((~$true) <=> $false),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(210,plain,
% 1.48/1.69 (((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0)) <=> $true),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(211,plain,
% 1.48/1.69 ((~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) <=> (~$true)),
% 1.48/1.69 inference(monotonicity,[status(thm)],[210])).
% 1.48/1.69 tff(212,plain,
% 1.48/1.69 ((~((~(u1_struct_0(A!0) = k1_xboole_0)) | (u1_struct_0(A!0) = k1_xboole_0))) <=> $false),
% 1.48/1.69 inference(transitivity,[status(thm)],[211, 209])).
% 1.48/1.69 tff(213,plain,
% 1.48/1.69 ((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))))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[212])).
% 1.48/1.69 tff(214,plain,
% 1.48/1.69 ((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))))),
% 1.48/1.69 inference(transitivity,[status(thm)],[213, 208])).
% 1.48/1.69 tff(215,plain,
% 1.48/1.69 (((~![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)))))),
% 1.48/1.69 inference(monotonicity,[status(thm)],[214])).
% 1.48/1.69 tff(216,plain,
% 1.48/1.69 (((~![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))))),
% 1.48/1.69 inference(transitivity,[status(thm)],[215, 207])).
% 1.48/1.69 tff(217,plain,
% 1.48/1.69 ((~![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))))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(218,plain,
% 1.48/1.69 ((~![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)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.48/1.69 tff(219,plain,
% 1.48/1.69 (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)))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[218, 206])).
% 1.48/1.69 tff(220,plain,
% 1.48/1.69 (r2_hidden(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[219, 193, 154, 132])).
% 1.48/1.69 tff(221,plain,
% 1.48/1.69 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(222,plain,
% 1.48/1.69 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[221])).
% 1.48/1.69 tff(223,plain,
% 1.48/1.69 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(224,plain,
% 1.48/1.69 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 1.48/1.69 inference(bind,[status(th)],[])).
% 1.48/1.69 tff(225,plain,
% 1.48/1.69 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(quant_intro,[status(thm)],[224])).
% 1.48/1.69 tff(226,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 1.48/1.69 tff(227,plain,
% 1.48/1.69 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.48/1.69 tff(228,plain,
% 1.48/1.69 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[227, 223])).
% 1.48/1.69 tff(229,plain,(
% 1.48/1.69 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(skolemize,[status(sab)],[228])).
% 1.48/1.69 tff(230,plain,
% 1.48/1.69 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[229, 222])).
% 1.48/1.69 tff(231,plain,
% 1.48/1.69 (((~![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))))),
% 1.48/1.69 inference(rewrite,[status(thm)],[])).
% 1.48/1.69 tff(232,plain,
% 1.48/1.69 ((~![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))))),
% 1.48/1.69 inference(quant_inst,[status(thm)],[])).
% 1.48/1.69 tff(233,plain,
% 1.48/1.69 ((~![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)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.48/1.69 tff(234,plain,
% 1.48/1.69 (m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[233, 230, 220])).
% 1.48/1.69 tff(235,plain,
% 1.48/1.69 ((~(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))))),
% 1.48/1.69 inference(tautology,[status(thm)],[])).
% 1.48/1.69 tff(236,plain,
% 1.48/1.69 ((~(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)))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[235, 234])).
% 1.48/1.69 tff(237,plain,
% 1.48/1.69 (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)))),
% 1.48/1.69 inference(unit_resolution,[status(thm)],[236, 105])).
% 1.48/1.69 tff(238,plain,
% 1.48/1.69 (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)))),
% 1.48/1.69 inference(modus_ponens,[status(thm)],[237, 62])).
% 1.48/1.69 tff(239,plain,
% 1.48/1.69 (^[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)))))))))))))))))))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(240,plain,
% 1.54/1.69 (![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)))))))))))))))))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[239])).
% 1.54/1.69 tff(241,plain,
% 1.54/1.69 (^[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))))))))))))))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(242,plain,
% 1.54/1.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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)))))))))))))))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[241])).
% 1.54/1.70 tff(243,plain,
% 1.54/1.70 (^[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))))))))))))))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(244,plain,
% 1.54/1.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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)))))))))))))))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[243])).
% 1.54/1.70 tff(245,plain,
% 1.54/1.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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)))))))))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[244, 242])).
% 1.54/1.70 tff(246,plain,
% 1.54/1.70 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), 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)))))))))))))))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(247,plain,
% 1.54/1.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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)))))))))))))))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[246])).
% 1.54/1.70 tff(248,plain,
% 1.54/1.70 (^[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))))))))))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(249,plain,
% 1.54/1.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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)))))))))))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[248])).
% 1.54/1.70 tff(250,plain,
% 1.54/1.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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)))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(251,plain,
% 1.54/1.70 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : 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)))))))))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(252,plain,
% 1.54/1.70 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_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)))))))))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[251])).
% 1.54/1.70 tff(253,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/sandbox2/benchmark/theBenchmark.p','d4_autgroup')).
% 1.54/1.70 tff(254,plain,
% 1.54/1.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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)))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.54/1.70 tff(255,plain,
% 1.54/1.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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)))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[254, 250])).
% 1.54/1.70 tff(256,plain,(
% 1.54/1.70 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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))))))))))))),
% 1.54/1.70 inference(skolemize,[status(sab)],[255])).
% 1.54/1.70 tff(257,plain,
% 1.54/1.70 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_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)))))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[256, 249])).
% 1.54/1.70 tff(258,plain,
% 1.54/1.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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)))))))))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[257, 247])).
% 1.54/1.70 tff(259,plain,
% 1.54/1.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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)))))))))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[258, 245])).
% 1.54/1.70 tff(260,plain,
% 1.54/1.70 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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)))))))))))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[259, 240])).
% 1.54/1.70 tff(261,plain,
% 1.54/1.70 (v4_group_1(A!0)),
% 1.54/1.70 inference(and_elim,[status(thm)],[19])).
% 1.54/1.70 tff(262,plain,
% 1.54/1.70 (v3_group_1(A!0)),
% 1.54/1.70 inference(and_elim,[status(thm)],[19])).
% 1.54/1.70 tff(263,plain,
% 1.54/1.70 (v1_group_1(A!0)),
% 1.54/1.70 inference(and_elim,[status(thm)],[19])).
% 1.54/1.70 tff(264,plain,
% 1.54/1.70 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))) <=> ((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(265,plain,
% 1.54/1.71 ((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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) <=> (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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(266,plain,
% 1.54/1.71 (^[B: $i] : rewrite(((~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(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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(267,plain,
% 1.54/1.71 (![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)))))))))))))))) <=> ![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))),
% 1.54/1.71 inference(quant_intro,[status(thm)],[266])).
% 1.54/1.71 tff(268,plain,
% 1.54/1.71 ((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) | (~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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[267])).
% 1.54/1.71 tff(269,plain,
% 1.54/1.71 ((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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[268, 265])).
% 1.54/1.71 tff(270,plain,
% 1.54/1.71 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = 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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[269])).
% 1.54/1.71 tff(271,plain,
% 1.54/1.71 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = 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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[270, 264])).
% 1.54/1.72 tff(272,plain,
% 1.54/1.72 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = 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)))))))))))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(273,plain,
% 1.54/1.72 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = 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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.54/1.72 tff(274,plain,
% 1.54/1.72 (![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[273, 38, 263, 262, 261, 20, 260])).
% 1.54/1.72 tff(275,plain,
% 1.54/1.72 (^[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))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(276,plain,
% 1.54/1.72 (![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)))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[275])).
% 1.54/1.72 tff(277,plain,
% 1.54/1.72 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(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)))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(278,plain,
% 1.54/1.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(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)))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[277])).
% 1.54/1.72 tff(279,plain,
% 1.54/1.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(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)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(280,plain,
% 1.54/1.72 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(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)))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(281,plain,
% 1.54/1.72 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(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)))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[280])).
% 1.54/1.72 tff(282,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 1.54/1.72 tff(283,plain,
% 1.54/1.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.54/1.72 tff(284,plain,
% 1.54/1.72 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[283, 279])).
% 1.54/1.72 tff(285,plain,(
% 1.54/1.72 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.54/1.72 inference(skolemize,[status(sab)],[284])).
% 1.54/1.72 tff(286,plain,
% 1.54/1.72 (![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)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[285, 278])).
% 1.54/1.72 tff(287,plain,
% 1.54/1.72 (![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)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[286, 276])).
% 1.54/1.72 tff(288,plain,
% 1.54/1.72 (((~![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)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(289,plain,
% 1.54/1.72 ((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)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(290,plain,
% 1.54/1.72 (((~![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))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[289])).
% 1.54/1.72 tff(291,plain,
% 1.54/1.72 (((~![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)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[290, 288])).
% 1.54/1.72 tff(292,plain,
% 1.54/1.72 ((~![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)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(293,plain,
% 1.54/1.72 ((~![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))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[292, 291])).
% 1.54/1.72 tff(294,plain,
% 1.54/1.72 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[293, 38, 263, 262, 261, 20, 287])).
% 1.54/1.72 tff(295,plain,
% 1.54/1.72 (((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | ((~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)) | ![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))))))) | (~((~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)))))))))))))) <=> ((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | (~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)) | ![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))))))) | (~((~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)))))))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(296,plain,
% 1.54/1.72 (((~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)) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(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)) | ![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))))))) | (~((~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)))))))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(297,plain,
% 1.54/1.72 (((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | ((~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)) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | ((~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)) | ![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))))))) | (~((~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))))))))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[296])).
% 1.54/1.72 tff(298,plain,
% 1.54/1.72 (((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | ((~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)) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | (~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)) | ![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))))))) | (~((~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)))))))))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[297, 295])).
% 1.54/1.73 tff(299,plain,
% 1.54/1.73 ((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | ((~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)) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(k4_autgroup(A!0), A!0), k4_autgroup(A!0)))))))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(300,plain,
% 1.54/1.73 ((~![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) | ![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))))))) | (~((~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)))))))))))))) | (~((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))))))) | (~((~((~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))))))) | r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) | (~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)) | ![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))))))) | (~((~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))))))))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.54/1.73 tff(301,plain,
% 1.54/1.73 (![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)) | ![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))))))) | (~((~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))))))))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[300, 294, 274])).
% 1.54/1.73 tff(302,plain,
% 1.54/1.73 (((~![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)) | ![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))))))) | (~((~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))))))))))))) | ((~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)) | ![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))) | (~((~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))))))))))))) <=> ((~![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)) | ![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))))))) | (~((~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))))))))))))) | (~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)) | ![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))) | (~((~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))))))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(303,plain,
% 1.54/1.73 ((~![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)) | ![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))))))) | (~((~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))))))))))))) | ((~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)) | ![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))) | (~((~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))))))))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(304,plain,
% 1.54/1.73 ((~![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)) | ![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))))))) | (~((~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))))))))))))) | (~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)) | ![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))) | (~((~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)))))))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.54/1.73 tff(305,plain,
% 1.54/1.73 ((~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)) | ![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))) | (~((~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)))))))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[304, 301])).
% 1.54/1.73 tff(306,plain,
% 1.54/1.73 (~((~(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))) | (~((~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))))))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[305, 238])).
% 1.54/1.73 tff(307,plain,
% 1.54/1.73 (((~(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))) | (~((~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))))))),
% 1.54/1.73 inference(tautology,[status(thm)],[])).
% 1.54/1.73 tff(308,plain,
% 1.54/1.73 (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)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[307, 306])).
% 1.54/1.73 tff(309,plain,
% 1.54/1.73 (((~![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))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(310,plain,
% 1.54/1.73 ((~![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))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(311,plain,
% 1.54/1.73 ((~![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)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[310, 309])).
% 1.54/1.73 tff(312,plain,
% 1.54/1.73 (![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)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[311, 98, 46, 294])).
% 1.54/1.73 tff(313,plain,
% 1.54/1.73 ((~![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)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(314,plain,
% 1.54/1.73 (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))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[313, 312])).
% 1.54/1.73 tff(315,plain,
% 1.54/1.73 (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))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[115])).
% 1.54/1.73 tff(316,plain,
% 1.54/1.73 (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))),
% 1.54/1.73 inference(symmetry,[status(thm)],[315])).
% 1.54/1.73 tff(317,plain,
% 1.54/1.73 ((~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)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[316])).
% 1.54/1.73 tff(318,plain,
% 1.54/1.73 (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 1.54/1.73 inference(or_elim,[status(thm)],[18])).
% 1.54/1.73 tff(319,plain,
% 1.54/1.73 (~m2_fraenkel(k6_relat_1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.54/1.73 tff(320,plain,
% 1.54/1.73 ((~(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)))),
% 1.54/1.73 inference(tautology,[status(thm)],[])).
% 1.54/1.73 tff(321,plain,
% 1.54/1.73 (~m1_subset_1(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[320, 319, 314])).
% 1.54/1.73 tff(322,plain,
% 1.54/1.73 (((~![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)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(323,plain,
% 1.54/1.73 ((~![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)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(324,plain,
% 1.54/1.73 ((~![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))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[323, 322])).
% 1.54/1.73 tff(325,plain,
% 1.54/1.73 ((~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))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[324, 230])).
% 1.54/1.73 tff(326,plain,
% 1.54/1.73 (~r2_hidden(k6_relat_1(u1_struct_0(A!0)), k4_autgroup(A!0))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[325, 321])).
% 1.54/1.73 tff(327,plain,
% 1.54/1.73 ((~(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)))))),
% 1.54/1.73 inference(tautology,[status(thm)],[])).
% 1.54/1.73 tff(328,plain,
% 1.54/1.73 ((~(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)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[327, 326])).
% 1.54/1.73 tff(329,plain,
% 1.54/1.73 (![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)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[328, 308])).
% 1.54/1.73 tff(330,plain,
% 1.54/1.73 (^[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))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(331,plain,
% 1.54/1.73 (![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)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[330])).
% 1.54/1.73 tff(332,plain,
% 1.54/1.73 (^[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)))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(333,plain,
% 1.54/1.73 (![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)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[332])).
% 1.54/1.73 tff(334,plain,
% 1.54/1.73 (![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)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(335,plain,
% 1.54/1.73 (^[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))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(336,plain,
% 1.54/1.73 (![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)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[335])).
% 1.54/1.73 tff(337,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_group_1')).
% 1.54/1.73 tff(338,plain,
% 1.54/1.73 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.54/1.73 tff(339,plain,
% 1.54/1.73 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[338, 334])).
% 1.54/1.73 tff(340,plain,(
% 1.54/1.73 ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 1.54/1.73 inference(skolemize,[status(sab)],[339])).
% 1.54/1.73 tff(341,plain,
% 1.54/1.73 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[340, 333])).
% 1.54/1.73 tff(342,plain,
% 1.54/1.73 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[341, 331])).
% 1.54/1.73 tff(343,plain,
% 1.54/1.73 (((~![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)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(344,plain,
% 1.54/1.74 ((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)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(345,plain,
% 1.54/1.74 (((~![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))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[344])).
% 1.54/1.74 tff(346,plain,
% 1.54/1.74 (((~![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)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[345, 343])).
% 1.54/1.74 tff(347,plain,
% 1.54/1.74 ((~![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)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(348,plain,
% 1.54/1.74 ((~![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))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[347, 346])).
% 1.54/1.74 tff(349,plain,
% 1.54/1.74 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[348, 38, 20, 342])).
% 1.54/1.74 tff(350,plain,
% 1.54/1.74 (((~![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))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(351,plain,
% 1.54/1.74 ((~![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))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(352,plain,
% 1.54/1.74 ((~![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)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.54/1.74 tff(353,plain,
% 1.54/1.74 (~((~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))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[352, 349, 329])).
% 1.54/1.74 tff(354,plain,
% 1.54/1.74 (((~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))),
% 1.54/1.74 inference(tautology,[status(thm)],[])).
% 1.54/1.74 tff(355,plain,
% 1.54/1.74 (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))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[354, 353])).
% 1.54/1.74 tff(356,plain,
% 1.54/1.74 (^[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))))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(357,plain,
% 1.54/1.74 (![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)))))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[356])).
% 1.54/1.74 tff(358,plain,
% 1.54/1.74 (^[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))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(359,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[358])).
% 1.54/1.74 tff(360,plain,
% 1.54/1.74 (^[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))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(361,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[360])).
% 1.54/1.74 tff(362,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[361, 359])).
% 1.54/1.74 tff(363,plain,
% 1.54/1.74 (^[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)))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(364,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[363])).
% 1.54/1.74 tff(365,plain,
% 1.54/1.74 (![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)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(366,plain,
% 1.54/1.74 (^[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)))))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(367,plain,
% 1.54/1.74 (![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)))))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[366])).
% 1.54/1.74 tff(368,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/sandbox2/benchmark/theBenchmark.p','d2_group_3')).
% 1.54/1.74 tff(369,plain,
% 1.54/1.74 (![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)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.54/1.74 tff(370,plain,
% 1.54/1.74 (![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)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[369, 365])).
% 1.54/1.74 tff(371,plain,(
% 1.54/1.74 ![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)))))),
% 1.54/1.74 inference(skolemize,[status(sab)],[370])).
% 1.54/1.74 tff(372,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[371, 364])).
% 1.54/1.74 tff(373,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[372, 362])).
% 1.54/1.74 tff(374,plain,
% 1.54/1.74 (![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)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[373, 357])).
% 1.54/1.74 tff(375,plain,
% 1.54/1.74 (((~![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)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(376,plain,
% 1.54/1.74 ((~![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)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(377,plain,
% 1.54/1.74 ((~![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))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.54/1.74 tff(378,plain,
% 1.54/1.74 (![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))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[377, 38, 262, 261, 20, 374])).
% 1.54/1.74 tff(379,plain,
% 1.54/1.74 (((~![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))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(380,plain,
% 1.54/1.74 ((~![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))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(381,plain,
% 1.54/1.74 ((~![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)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.54/1.74 tff(382,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[381, 378, 355])).
% 1.54/1.74 tff(383,plain,
% 1.54/1.74 (((~![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))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(384,plain,
% 1.54/1.74 ((~![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))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(385,plain,
% 1.54/1.74 ((~![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)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.54/1.74 tff(386,plain,
% 1.54/1.74 (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))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[385, 349, 382])).
% 1.54/1.74 tff(387,plain,
% 1.54/1.74 (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))),
% 1.54/1.74 inference(symmetry,[status(thm)],[386])).
% 1.54/1.74 tff(388,plain,
% 1.54/1.74 (^[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))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(389,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[388])).
% 1.54/1.74 tff(390,plain,
% 1.54/1.74 (^[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)))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(391,plain,
% 1.54/1.74 (![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)))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[390])).
% 1.54/1.74 tff(392,plain,
% 1.54/1.74 (![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))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(393,plain,
% 1.54/1.74 (^[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))))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(394,plain,
% 1.54/1.74 (![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))))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[393])).
% 1.54/1.74 tff(395,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/sandbox2/benchmark/theBenchmark.p','cc1_group_1')).
% 1.54/1.74 tff(396,plain,
% 1.54/1.74 (![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[395, 394])).
% 1.54/1.74 tff(397,plain,
% 1.54/1.74 (![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[396, 392])).
% 1.54/1.74 tff(398,plain,(
% 1.54/1.74 ![A: $i] : (((~v3_struct_0(A)) & v2_group_1(A)) | (~l1_group_1(A)) | (~((~v3_struct_0(A)) & v3_group_1(A))))),
% 1.54/1.74 inference(skolemize,[status(sab)],[397])).
% 1.54/1.74 tff(399,plain,
% 1.54/1.74 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[398, 391])).
% 1.54/1.74 tff(400,plain,
% 1.54/1.74 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~(v3_struct_0(A) | (~v2_group_1(A)))) | (~v3_group_1(A)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[399, 389])).
% 1.54/1.74 tff(401,plain,
% 1.54/1.74 (((~![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)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(402,plain,
% 1.54/1.74 ((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)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(403,plain,
% 1.54/1.74 (((~![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))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[402])).
% 1.54/1.74 tff(404,plain,
% 1.54/1.74 (((~![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)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[403, 401])).
% 1.54/1.74 tff(405,plain,
% 1.54/1.74 ((~![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)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(406,plain,
% 1.54/1.74 ((~![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))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.54/1.74 tff(407,plain,
% 1.54/1.74 (~(v3_struct_0(A!0) | (~v2_group_1(A!0)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[406, 38, 262, 20, 400])).
% 1.54/1.74 tff(408,plain,
% 1.54/1.74 ((v3_struct_0(A!0) | (~v2_group_1(A!0))) | v2_group_1(A!0)),
% 1.54/1.74 inference(tautology,[status(thm)],[])).
% 1.54/1.74 tff(409,plain,
% 1.54/1.74 (v2_group_1(A!0)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[408, 407])).
% 1.54/1.74 tff(410,plain,
% 1.54/1.74 (^[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))))))))))))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(411,plain,
% 1.54/1.74 (![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)))))))))))))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[410])).
% 1.54/1.74 tff(412,plain,
% 1.54/1.74 (^[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))))))))))))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(413,plain,
% 1.54/1.74 (![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)))))))))))))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[412])).
% 1.54/1.74 tff(414,plain,
% 1.54/1.74 (![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)))))))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[413, 411])).
% 1.54/1.74 tff(415,plain,
% 1.54/1.74 (^[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)))))))))))))))),
% 1.54/1.74 inference(bind,[status(th)],[])).
% 1.54/1.74 tff(416,plain,
% 1.54/1.74 (![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)))))))))))))),
% 1.54/1.74 inference(quant_intro,[status(thm)],[415])).
% 1.54/1.74 tff(417,plain,
% 1.54/1.74 (^[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))))))))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(418,plain,
% 1.54/1.75 (![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)))))))))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[417])).
% 1.54/1.75 tff(419,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(420,plain,
% 1.54/1.75 (^[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)))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(421,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[420])).
% 1.54/1.75 tff(422,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/sandbox2/benchmark/theBenchmark.p','d5_group_1')).
% 1.54/1.75 tff(423,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.54/1.75 tff(424,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[423, 419])).
% 1.54/1.75 tff(425,plain,(
% 1.54/1.75 ![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)))),
% 1.54/1.75 inference(skolemize,[status(sab)],[424])).
% 1.54/1.75 tff(426,plain,
% 1.54/1.75 (![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)))))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[425, 418])).
% 1.54/1.75 tff(427,plain,
% 1.54/1.75 (![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)))))))))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[426, 416])).
% 1.54/1.75 tff(428,plain,
% 1.54/1.75 (![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)))))))))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[427, 414])).
% 1.54/1.75 tff(429,plain,
% 1.54/1.75 (((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(430,plain,
% 1.54/1.75 ((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))))))))))))) <=> (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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(431,plain,
% 1.54/1.75 (((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[430])).
% 1.54/1.75 tff(432,plain,
% 1.54/1.75 (((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[431, 429])).
% 1.54/1.75 tff(433,plain,
% 1.54/1.75 ((~![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)))))))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(434,plain,
% 1.54/1.75 ((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.54/1.75 tff(435,plain,
% 1.54/1.75 ((~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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[434, 38, 20, 428])).
% 1.54/1.75 tff(436,plain,
% 1.54/1.75 (![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))))))) | (~((~((~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))))))) | (B = k2_group_1(A!0)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[435, 409])).
% 1.54/1.75 tff(437,plain,
% 1.54/1.75 (((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(438,plain,
% 1.54/1.75 (((~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))))))) | (~((~((~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))))))) | (k2_group_1(A!0) = k2_group_1(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))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(439,plain,
% 1.54/1.75 (((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))) | (~((~((~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))))))) | (k2_group_1(A!0) = k2_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))))))) | (~((~((~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))))))) | (B = k2_group_1(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)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[438])).
% 1.54/1.75 tff(440,plain,
% 1.54/1.75 (((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))) | (~((~((~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))))))) | (k2_group_1(A!0) = k2_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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[439, 437])).
% 1.54/1.75 tff(441,plain,
% 1.54/1.75 ((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(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))))))) | (~((~((~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))))))) | (k2_group_1(A!0) = k2_group_1(A!0)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(442,plain,
% 1.54/1.75 ((~![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))))))) | (~((~((~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))))))) | (B = k2_group_1(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)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.54/1.75 tff(443,plain,
% 1.54/1.75 (![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)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[442, 349, 436])).
% 1.54/1.75 tff(444,plain,
% 1.54/1.75 (((~![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))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(445,plain,
% 1.54/1.75 ((~![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))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(446,plain,
% 1.54/1.75 ((~![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)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[445, 444])).
% 1.54/1.75 tff(447,plain,
% 1.54/1.75 (~((~(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))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[446, 443, 355])).
% 1.54/1.75 tff(448,plain,
% 1.54/1.75 (((~(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))),
% 1.54/1.75 inference(tautology,[status(thm)],[])).
% 1.54/1.75 tff(449,plain,
% 1.54/1.75 (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)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[448, 447])).
% 1.54/1.75 tff(450,plain,
% 1.54/1.75 (^[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))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(451,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[450])).
% 1.54/1.75 tff(452,plain,
% 1.54/1.75 (^[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)))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(453,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[452])).
% 1.54/1.75 tff(454,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(455,plain,
% 1.54/1.75 (^[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)))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(456,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[455])).
% 1.54/1.76 tff(457,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/sandbox2/benchmark/theBenchmark.p','t16_group_1')).
% 1.54/1.76 tff(458,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.54/1.76 tff(459,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[458, 454])).
% 1.54/1.76 tff(460,plain,(
% 1.54/1.76 ![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)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[459])).
% 1.54/1.76 tff(461,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[460, 453])).
% 1.54/1.76 tff(462,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[461, 451])).
% 1.54/1.76 tff(463,plain,
% 1.54/1.76 (((~![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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(464,plain,
% 1.54/1.76 ((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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(465,plain,
% 1.54/1.76 (((~![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))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[464])).
% 1.54/1.76 tff(466,plain,
% 1.54/1.76 (((~![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)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[465, 463])).
% 1.54/1.76 tff(467,plain,
% 1.54/1.76 ((~![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)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(468,plain,
% 1.54/1.76 ((~![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))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.54/1.76 tff(469,plain,
% 1.54/1.76 (k3_group_1(A!0, k2_group_1(A!0)) = k2_group_1(A!0)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[468, 38, 262, 261, 20, 462])).
% 1.54/1.76 tff(470,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[469])).
% 1.54/1.76 tff(471,plain,
% 1.54/1.76 (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)),
% 1.54/1.76 inference(transitivity,[status(thm)],[470, 449])).
% 1.54/1.76 tff(472,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[471])).
% 1.54/1.76 tff(473,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(symmetry,[status(thm)],[472])).
% 1.54/1.76 tff(474,plain,
% 1.54/1.76 (((~(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))),
% 1.54/1.76 inference(tautology,[status(thm)],[])).
% 1.54/1.76 tff(475,plain,
% 1.54/1.76 (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)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[474, 447])).
% 1.54/1.76 tff(476,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(symmetry,[status(thm)],[475])).
% 1.54/1.76 tff(477,plain,
% 1.54/1.76 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(478,plain,
% 1.54/1.76 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[477])).
% 1.54/1.76 tff(479,plain,
% 1.54/1.76 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(480,plain,
% 1.54/1.76 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(481,plain,
% 1.54/1.76 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[480])).
% 1.54/1.76 tff(482,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 1.54/1.76 tff(483,plain,
% 1.54/1.76 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[482, 481])).
% 1.54/1.76 tff(484,plain,
% 1.54/1.76 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[483, 479])).
% 1.54/1.76 tff(485,plain,(
% 1.54/1.76 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[484])).
% 1.54/1.76 tff(486,plain,
% 1.54/1.76 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[485, 478])).
% 1.54/1.76 tff(487,plain,
% 1.54/1.76 (((~![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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(488,plain,
% 1.54/1.76 ((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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(489,plain,
% 1.54/1.76 (((~![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))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[488])).
% 1.54/1.76 tff(490,plain,
% 1.54/1.76 (((~![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)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[489, 487])).
% 1.54/1.76 tff(491,plain,
% 1.54/1.76 ((~![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))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(492,plain,
% 1.54/1.76 ((~![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))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.54/1.76 tff(493,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[492, 486, 46, 355])).
% 1.54/1.76 tff(494,plain,
% 1.54/1.76 (^[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)))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(495,plain,
% 1.54/1.76 (![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))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[494])).
% 1.54/1.76 tff(496,plain,
% 1.54/1.76 (![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))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(497,plain,
% 1.54/1.76 (^[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)))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(498,plain,
% 1.54/1.76 (![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))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[497])).
% 1.54/1.76 tff(499,axiom,(![A: $i, B: $i] : (r2_hidden(B, A) => (k1_funct_1(k6_relat_1(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_funct_1')).
% 1.54/1.76 tff(500,plain,
% 1.54/1.76 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.54/1.76 tff(501,plain,
% 1.54/1.76 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[500, 496])).
% 1.54/1.76 tff(502,plain,(
% 1.54/1.76 ![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 1.54/1.76 inference(skolemize,[status(sab)],[501])).
% 1.54/1.76 tff(503,plain,
% 1.54/1.76 (![A: $i, B: $i] : ((~r2_hidden(B, A)) | (k1_funct_1(k6_relat_1(A), B) = B))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[502, 495])).
% 1.54/1.76 tff(504,plain,
% 1.54/1.76 (((~![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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(505,plain,
% 1.54/1.76 ((~![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)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(506,plain,
% 1.54/1.76 ((~![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))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[505, 504])).
% 1.54/1.76 tff(507,plain,
% 1.54/1.76 (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)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[506, 503, 493])).
% 1.54/1.76 tff(508,plain,
% 1.54/1.76 (^[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))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(509,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[508])).
% 1.54/1.76 tff(510,plain,
% 1.54/1.76 (^[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)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(511,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[510])).
% 1.54/1.76 tff(512,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(513,plain,
% 1.54/1.76 (^[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)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(514,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[513])).
% 1.54/1.76 tff(515,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/sandbox2/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 1.54/1.76 tff(516,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.54/1.76 tff(517,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[516, 512])).
% 1.54/1.76 tff(518,plain,(
% 1.54/1.76 ![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)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[517])).
% 1.54/1.76 tff(519,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[518, 511])).
% 1.54/1.76 tff(520,plain,
% 1.54/1.76 (![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[519, 509])).
% 1.54/1.76 tff(521,plain,
% 1.54/1.76 (((~![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))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(522,plain,
% 1.54/1.76 ((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))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(523,plain,
% 1.54/1.76 (((~![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)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[522])).
% 1.54/1.76 tff(524,plain,
% 1.54/1.76 (((~![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))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[523, 521])).
% 1.54/1.76 tff(525,plain,
% 1.54/1.76 ((~![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))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(526,plain,
% 1.54/1.76 ((~![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)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.54/1.76 tff(527,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[526, 520, 46, 154, 193, 170, 355])).
% 1.54/1.76 tff(528,plain,
% 1.54/1.76 (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))),
% 1.54/1.76 inference(transitivity,[status(thm)],[527, 507, 476, 473, 387])).
% 1.54/1.76 tff(529,plain,
% 1.54/1.76 (((~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))))),
% 1.63/1.78 inference(tautology,[status(thm)],[])).
% 1.63/1.78 tff(530,plain,
% 1.63/1.78 (~(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)))),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[529, 353])).
% 1.63/1.78 tff(531,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[530, 528])).
% 1.63/1.78 % SZS output end Proof
% 1.63/1.78 % E exiting
%------------------------------------------------------------------------------