%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP630+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:08:13 AM UTC 2025
% Result : Theorem 216.65s 216.91s
% Output : Proof 216.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP630+1 : TPTP v9.0.0. Released v3.4.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 16:32:31 EDT 2025
% 0.14/0.36 % CPUTime :
% 216.65/216.91 % SZS status Theorem
% 216.65/216.91 % SZS output start Proof
% 216.65/216.91 tff(k6_partfun1_type, type, (
% 216.65/216.91 k6_partfun1: $i > $i)).
% 216.65/216.91 tff(u1_struct_0_type, type, (
% 216.65/216.91 u1_struct_0: $i > $i)).
% 216.65/216.91 tff(tptp_fun_A_0_type, type, (
% 216.65/216.91 tptp_fun_A_0: $i)).
% 216.65/216.91 tff(k1_partfun1_type, type, (
% 216.65/216.91 k1_partfun1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 216.65/216.91 tff(k6_autgroup_type, type, (
% 216.65/216.91 k6_autgroup: ( $i * $i ) > $i)).
% 216.65/216.91 tff(k3_group_1_type, type, (
% 216.65/216.91 k3_group_1: ( $i * $i ) > $i)).
% 216.65/216.91 tff(tptp_fun_B_1_type, type, (
% 216.65/216.91 tptp_fun_B_1: $i)).
% 216.65/216.91 tff(k2_group_1_type, type, (
% 216.65/216.91 k2_group_1: $i > $i)).
% 216.65/216.91 tff(v4_group_1_type, type, (
% 216.65/216.91 v4_group_1: $i > $o)).
% 216.65/216.91 tff(v3_group_1_type, type, (
% 216.65/216.91 v3_group_1: $i > $o)).
% 216.65/216.91 tff(l1_group_1_type, type, (
% 216.65/216.91 l1_group_1: $i > $o)).
% 216.65/216.91 tff(v1_group_1_type, type, (
% 216.65/216.91 v1_group_1: $i > $o)).
% 216.65/216.91 tff(v3_struct_0_type, type, (
% 216.65/216.91 v3_struct_0: $i > $o)).
% 216.65/216.91 tff(k2_funct_1_type, type, (
% 216.65/216.91 k2_funct_1: $i > $i)).
% 216.65/216.91 tff(m1_subset_1_type, type, (
% 216.65/216.91 m1_subset_1: ( $i * $i ) > $o)).
% 216.65/216.91 tff(k7_funct_2_type, type, (
% 216.65/216.91 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 216.65/216.91 tff(k5_relat_1_type, type, (
% 216.65/216.91 k5_relat_1: ( $i * $i ) > $i)).
% 216.65/216.91 tff(m1_relset_1_type, type, (
% 216.65/216.91 m1_relset_1: ( $i * $i * $i ) > $o)).
% 216.65/216.91 tff(m2_relset_1_type, type, (
% 216.65/216.91 m2_relset_1: ( $i * $i * $i ) > $o)).
% 216.65/216.91 tff(v1_group_6_type, type, (
% 216.65/216.91 v1_group_6: ( $i * $i * $i ) > $o)).
% 216.65/216.91 tff(v1_funct_2_type, type, (
% 216.65/216.91 v1_funct_2: ( $i * $i * $i ) > $o)).
% 216.65/216.91 tff(v1_funct_1_type, type, (
% 216.65/216.91 v1_funct_1: $i > $o)).
% 216.65/216.91 tff(m2_fraenkel_type, type, (
% 216.65/216.91 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 216.65/216.91 tff(k1_autgroup_type, type, (
% 216.65/216.91 k1_autgroup: $i > $i)).
% 216.65/216.91 tff(k4_autgroup_type, type, (
% 216.65/216.91 k4_autgroup: $i > $i)).
% 216.65/216.91 tff(r2_hidden_type, type, (
% 216.65/216.91 r2_hidden: ( $i * $i ) > $o)).
% 216.65/216.91 tff(v3_group_6_type, type, (
% 216.65/216.91 v3_group_6: ( $i * $i * $i ) > $o)).
% 216.65/216.91 tff(v2_funct_1_type, type, (
% 216.65/216.91 v2_funct_1: $i > $o)).
% 216.65/216.91 tff(tptp_fun_C_3_type, type, (
% 216.65/216.91 tptp_fun_C_3: ( $i * $i ) > $i)).
% 216.65/216.91 tff(tptp_fun_C_2_type, type, (
% 216.65/216.91 tptp_fun_C_2: ( $i * $i ) > $i)).
% 216.65/216.91 tff(m1_fraenkel_type, type, (
% 216.65/216.91 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 216.65/216.91 tff(v1_xboole_0_type, type, (
% 216.65/216.91 v1_xboole_0: $i > $o)).
% 216.65/216.91 tff(l1_struct_0_type, type, (
% 216.65/216.91 l1_struct_0: $i > $o)).
% 216.65/216.91 tff(k1_xboole_0_type, type, (
% 216.65/216.91 k1_xboole_0: $i)).
% 216.65/216.91 tff(k2_relat_1_type, type, (
% 216.65/216.91 k2_relat_1: $i > $i)).
% 216.65/216.91 tff(k1_relat_1_type, type, (
% 216.65/216.91 k1_relat_1: $i > $i)).
% 216.65/216.91 tff(v1_fraenkel_type, type, (
% 216.65/216.91 v1_fraenkel: $i > $o)).
% 216.65/216.91 tff(1,plain,
% 216.65/216.91 (^[A: $i] : refl((v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(2,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[1])).
% 216.65/216.91 tff(3,plain,
% 216.65/216.91 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(4,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[3])).
% 216.65/216.91 tff(5,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(6,plain,
% 216.65/216.91 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(7,plain,
% 216.65/216.91 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[6])).
% 216.65/216.91 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_autgroup')).
% 216.65/216.91 tff(9,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[8, 7])).
% 216.65/216.91 tff(10,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[9, 5])).
% 216.65/216.91 tff(11,plain,(
% 216.65/216.91 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 216.65/216.91 inference(skolemize,[status(sab)],[10])).
% 216.65/216.91 tff(12,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[11, 4])).
% 216.65/216.91 tff(13,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[12, 2])).
% 216.65/216.91 tff(14,plain,
% 216.65/216.91 ((((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1)))))) <=> ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(15,plain,
% 216.65/216.91 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B))))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(16,plain,
% 216.65/216.91 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B))))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(17,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_autgroup')).
% 216.65/216.91 tff(18,plain,
% 216.65/216.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[17, 16])).
% 216.65/216.91 tff(19,plain,
% 216.65/216.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[18, 15])).
% 216.65/216.91 tff(20,plain,
% 216.65/216.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[19, 15])).
% 216.65/216.91 tff(21,plain,
% 216.65/216.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k6_autgroup(A, k3_group_1(A, B)) = k2_funct_1(k6_autgroup(A, B)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[20, 15])).
% 216.65/216.91 tff(22,plain,
% 216.65/216.91 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[21, 14])).
% 216.65/216.91 tff(23,plain,
% 216.65/216.91 (l1_group_1(A!0)),
% 216.65/216.91 inference(and_elim,[status(thm)],[22])).
% 216.65/216.91 tff(24,plain,
% 216.65/216.91 (v4_group_1(A!0)),
% 216.65/216.91 inference(and_elim,[status(thm)],[22])).
% 216.65/216.91 tff(25,plain,
% 216.65/216.91 (v3_group_1(A!0)),
% 216.65/216.91 inference(and_elim,[status(thm)],[22])).
% 216.65/216.91 tff(26,plain,
% 216.65/216.91 (v1_group_1(A!0)),
% 216.65/216.91 inference(and_elim,[status(thm)],[22])).
% 216.65/216.91 tff(27,plain,
% 216.65/216.91 (~v3_struct_0(A!0)),
% 216.65/216.91 inference(and_elim,[status(thm)],[22])).
% 216.65/216.91 tff(28,plain,
% 216.65/216.91 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(29,plain,
% 216.65/216.91 ((v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(30,plain,
% 216.65/216.91 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.65/216.91 inference(monotonicity,[status(thm)],[29])).
% 216.65/216.91 tff(31,plain,
% 216.65/216.91 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))))),
% 216.65/216.91 inference(transitivity,[status(thm)],[30, 28])).
% 216.65/216.91 tff(32,plain,
% 216.65/216.91 ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 216.65/216.91 inference(quant_inst,[status(thm)],[])).
% 216.65/216.91 tff(33,plain,
% 216.65/216.91 ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0)))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[32, 31])).
% 216.65/216.91 tff(34,plain,
% 216.65/216.91 (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 216.65/216.91 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 216.65/216.91 tff(35,plain,
% 216.65/216.91 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(36,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[35])).
% 216.65/216.91 tff(37,plain,
% 216.65/216.91 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(38,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[37])).
% 216.65/216.91 tff(39,plain,
% 216.65/216.91 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(40,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[39])).
% 216.65/216.91 tff(41,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(transitivity,[status(thm)],[40, 38])).
% 216.65/216.91 tff(42,plain,
% 216.65/216.91 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(43,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[42])).
% 216.65/216.91 tff(44,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(45,plain,
% 216.65/216.91 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))))),
% 216.65/216.91 inference(bind,[status(th)],[])).
% 216.65/216.91 tff(46,plain,
% 216.65/216.91 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(quant_intro,[status(thm)],[45])).
% 216.65/216.91 tff(47,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_autgroup')).
% 216.65/216.91 tff(48,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[47, 46])).
% 216.65/216.91 tff(49,plain,
% 216.65/216.91 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[48, 44])).
% 216.65/216.91 tff(50,plain,(
% 216.65/216.91 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(skolemize,[status(sab)],[49])).
% 216.65/216.91 tff(51,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[50, 43])).
% 216.65/216.91 tff(52,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[51, 41])).
% 216.65/216.91 tff(53,plain,
% 216.65/216.91 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[52, 36])).
% 216.65/216.91 tff(54,plain,
% 216.65/216.91 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | (v3_struct_0(A!0) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | v3_struct_0(A!0) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(55,plain,
% 216.65/216.91 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) <=> (v3_struct_0(A!0) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(56,plain,
% 216.65/216.91 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | (v3_struct_0(A!0) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))))),
% 216.65/216.91 inference(monotonicity,[status(thm)],[55])).
% 216.65/216.91 tff(57,plain,
% 216.65/216.91 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | v3_struct_0(A!0) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 216.65/216.91 inference(transitivity,[status(thm)],[56, 54])).
% 216.65/216.91 tff(58,plain,
% 216.65/216.91 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))))),
% 216.65/216.91 inference(quant_inst,[status(thm)],[])).
% 216.65/216.91 tff(59,plain,
% 216.65/216.91 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, B), k6_autgroup(A, k3_group_1(A, B))) = k6_autgroup(A, k2_group_1(A)))))) | v3_struct_0(A!0) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))),
% 216.65/216.91 inference(modus_ponens,[status(thm)],[58, 57])).
% 216.65/216.91 tff(60,plain,
% 216.65/216.91 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 216.65/216.91 inference(unit_resolution,[status(thm)],[59, 27, 26, 25, 24, 23, 53])).
% 216.65/216.91 tff(61,plain,
% 216.65/216.91 (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))))),
% 216.65/216.91 inference(and_elim,[status(thm)],[22])).
% 216.65/216.91 tff(62,plain,
% 216.65/216.91 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 216.65/216.91 inference(or_elim,[status(thm)],[61])).
% 216.65/216.91 tff(63,plain,
% 216.65/216.91 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 216.65/216.91 inference(rewrite,[status(thm)],[])).
% 216.65/216.91 tff(64,plain,
% 216.65/216.91 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 216.65/216.92 inference(quant_inst,[status(thm)],[])).
% 216.65/216.92 tff(65,plain,
% 216.65/216.92 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B), k6_autgroup(A!0, k3_group_1(A!0, B))) = k6_autgroup(A!0, k2_group_1(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[64, 63])).
% 216.65/216.92 tff(66,plain,
% 216.65/216.92 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_autgroup(A!0, k2_group_1(A!0))),
% 216.65/216.92 inference(unit_resolution,[status(thm)],[65, 62, 60])).
% 216.65/216.92 tff(67,plain,
% 216.65/216.92 (^[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)))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(68,plain,
% 216.65/216.92 (![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))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[67])).
% 216.65/216.92 tff(69,plain,
% 216.65/216.92 (![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))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(70,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')).
% 216.65/216.92 tff(71,plain,
% 216.65/216.92 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[70, 69])).
% 216.65/216.92 tff(72,plain,(
% 216.65/216.92 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 216.65/216.92 inference(skolemize,[status(sab)],[71])).
% 216.65/216.92 tff(73,plain,
% 216.65/216.92 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[72, 68])).
% 216.65/216.92 tff(74,plain,
% 216.65/216.92 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 216.65/216.92 inference(quant_inst,[status(thm)],[])).
% 216.65/216.92 tff(75,plain,
% 216.65/216.92 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.92 inference(unit_resolution,[status(thm)],[74, 73])).
% 216.65/216.92 tff(76,plain,
% 216.65/216.92 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(77,plain,
% 216.65/216.92 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[76])).
% 216.65/216.92 tff(78,plain,
% 216.65/216.92 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(79,plain,
% 216.65/216.92 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[78])).
% 216.65/216.92 tff(80,plain,
% 216.65/216.92 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(81,plain,
% 216.65/216.92 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), ((((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(82,plain,
% 216.65/216.92 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[81])).
% 216.65/216.92 tff(83,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_autgroup')).
% 216.65/216.92 tff(84,plain,
% 216.65/216.92 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[83, 82])).
% 216.65/216.92 tff(85,plain,
% 216.65/216.92 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[84, 80])).
% 216.65/216.92 tff(86,plain,(
% 216.65/216.92 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 216.65/216.92 inference(skolemize,[status(sab)],[85])).
% 216.65/216.92 tff(87,plain,
% 216.65/216.92 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[86, 79])).
% 216.65/216.92 tff(88,plain,
% 216.65/216.92 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[87, 77])).
% 216.65/216.92 tff(89,plain,
% 216.65/216.92 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(90,plain,
% 216.65/216.92 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(91,plain,
% 216.65/216.92 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))))),
% 216.65/216.92 inference(monotonicity,[status(thm)],[90])).
% 216.65/216.92 tff(92,plain,
% 216.65/216.92 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 216.65/216.92 inference(transitivity,[status(thm)],[91, 89])).
% 216.65/216.92 tff(93,plain,
% 216.65/216.92 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 216.65/216.92 inference(quant_inst,[status(thm)],[])).
% 216.65/216.92 tff(94,plain,
% 216.65/216.92 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[93, 92])).
% 216.65/216.92 tff(95,plain,
% 216.65/216.92 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 216.65/216.92 inference(unit_resolution,[status(thm)],[94, 27, 26, 25, 24, 23, 62, 88])).
% 216.65/216.92 tff(96,plain,
% 216.65/216.92 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(97,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[96])).
% 216.65/216.92 tff(98,plain,
% 216.65/216.92 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(99,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[98])).
% 216.65/216.92 tff(100,plain,
% 216.65/216.92 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(101,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[100])).
% 216.65/216.92 tff(102,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.92 inference(transitivity,[status(thm)],[101, 99])).
% 216.65/216.92 tff(103,plain,
% 216.65/216.92 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(104,plain,
% 216.65/216.92 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[103])).
% 216.65/216.92 tff(105,plain,
% 216.65/216.92 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(106,plain,
% 216.65/216.92 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(107,plain,
% 216.65/216.92 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[106])).
% 216.65/216.92 tff(108,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_autgroup')).
% 216.65/216.92 tff(109,plain,
% 216.65/216.92 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[108, 107])).
% 216.65/216.92 tff(110,plain,
% 216.65/216.92 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[109, 105])).
% 216.65/216.92 tff(111,plain,(
% 216.65/216.92 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(skolemize,[status(sab)],[110])).
% 216.65/216.92 tff(112,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[111, 104])).
% 216.65/216.92 tff(113,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[112, 102])).
% 216.65/216.92 tff(114,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[113, 97])).
% 216.65/216.92 tff(115,plain,
% 216.65/216.92 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(116,plain,
% 216.65/216.92 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(117,plain,
% 216.65/216.92 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))),
% 216.65/216.92 inference(monotonicity,[status(thm)],[116])).
% 216.65/216.92 tff(118,plain,
% 216.65/216.92 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 216.65/216.92 inference(transitivity,[status(thm)],[117, 115])).
% 216.65/216.92 tff(119,plain,
% 216.65/216.92 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 216.65/216.92 inference(quant_inst,[status(thm)],[])).
% 216.65/216.92 tff(120,plain,
% 216.65/216.92 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[119, 118])).
% 216.65/216.92 tff(121,plain,
% 216.65/216.92 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 216.65/216.92 inference(unit_resolution,[status(thm)],[120, 27, 26, 25, 24, 23, 114])).
% 216.65/216.92 tff(122,plain,
% 216.65/216.92 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 216.65/216.92 inference(rewrite,[status(thm)],[])).
% 216.65/216.92 tff(123,plain,
% 216.65/216.92 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 216.65/216.92 inference(quant_inst,[status(thm)],[])).
% 216.65/216.92 tff(124,plain,
% 216.65/216.92 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 216.65/216.92 inference(modus_ponens,[status(thm)],[123, 122])).
% 216.65/216.92 tff(125,plain,
% 216.65/216.92 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 216.65/216.92 inference(unit_resolution,[status(thm)],[124, 121, 95])).
% 216.65/216.92 tff(126,plain,
% 216.65/216.92 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))))))))), rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(127,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), 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 = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.92 inference(quant_intro,[status(thm)],[126])).
% 216.65/216.92 tff(128,plain,
% 216.65/216.92 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))))),
% 216.65/216.92 inference(bind,[status(th)],[])).
% 216.65/216.92 tff(129,plain,
% 216.65/216.92 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), 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 = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 216.65/216.93 inference(quant_intro,[status(thm)],[128])).
% 216.65/216.93 tff(130,plain,
% 216.65/216.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))))),
% 216.65/216.93 inference(bind,[status(th)],[])).
% 216.65/216.93 tff(131,plain,
% 216.65/216.93 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), 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 = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 216.65/216.93 inference(quant_intro,[status(thm)],[130])).
% 216.65/216.93 tff(132,plain,
% 216.65/216.93 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), 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 = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 216.65/216.93 inference(transitivity,[status(thm)],[131, 129])).
% 216.65/216.93 tff(133,plain,
% 216.65/216.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))))),
% 216.65/216.93 inference(bind,[status(th)],[])).
% 216.65/216.93 tff(134,plain,
% 216.65/216.93 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 216.65/216.93 inference(quant_intro,[status(thm)],[133])).
% 216.65/216.93 tff(135,plain,
% 216.65/216.93 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))),
% 216.65/216.93 inference(bind,[status(th)],[])).
% 216.65/216.93 tff(136,plain,
% 216.65/216.93 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))),
% 216.65/216.93 inference(quant_intro,[status(thm)],[135])).
% 216.65/216.93 tff(137,plain,
% 216.65/216.93 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 216.65/216.93 inference(rewrite,[status(thm)],[])).
% 216.65/216.93 tff(138,plain,
% 216.65/216.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) <=> ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), rewrite((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), (![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))))),
% 216.65/216.93 inference(bind,[status(th)],[])).
% 216.65/216.93 tff(139,plain,
% 216.65/216.93 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 216.65/216.93 inference(quant_intro,[status(thm)],[138])).
% 216.65/216.93 tff(140,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_autgroup')).
% 216.65/216.93 tff(141,plain,
% 216.65/216.93 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 216.65/216.93 inference(modus_ponens,[status(thm)],[140, 139])).
% 216.65/216.93 tff(142,plain,
% 216.65/216.93 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 216.65/216.93 inference(modus_ponens,[status(thm)],[141, 137])).
% 216.65/216.93 tff(143,plain,(
% 216.65/216.93 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))),
% 216.65/216.93 inference(skolemize,[status(sab)],[142])).
% 216.65/216.93 tff(144,plain,
% 216.65/216.93 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))),
% 216.65/216.93 inference(modus_ponens,[status(thm)],[143, 136])).
% 216.65/216.93 tff(145,plain,
% 216.65/216.93 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 216.65/216.93 inference(modus_ponens,[status(thm)],[144, 134])).
% 216.65/216.93 tff(146,plain,
% 216.65/216.93 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 216.65/216.93 inference(modus_ponens,[status(thm)],[145, 132])).
% 216.65/216.93 tff(147,plain,
% 216.65/216.93 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.93 inference(modus_ponens,[status(thm)],[146, 127])).
% 216.65/216.93 tff(148,plain,
% 216.65/216.93 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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 = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.93 inference(rewrite,[status(thm)],[])).
% 216.65/216.93 tff(149,plain,
% 216.65/216.93 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.94 inference(rewrite,[status(thm)],[])).
% 216.65/216.94 tff(150,plain,
% 216.65/216.94 (^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.94 inference(bind,[status(th)],[])).
% 216.65/216.94 tff(151,plain,
% 216.65/216.94 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))),
% 216.65/216.94 inference(quant_intro,[status(thm)],[150])).
% 216.65/216.94 tff(152,plain,
% 216.65/216.94 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) <=> (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.94 inference(monotonicity,[status(thm)],[151])).
% 216.65/216.94 tff(153,plain,
% 216.65/216.94 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.94 inference(transitivity,[status(thm)],[152, 149])).
% 216.65/216.94 tff(154,plain,
% 216.65/216.94 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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 = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))))),
% 216.65/216.94 inference(monotonicity,[status(thm)],[153])).
% 216.65/216.94 tff(155,plain,
% 216.65/216.94 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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 = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.94 inference(transitivity,[status(thm)],[154, 148])).
% 216.65/216.94 tff(156,plain,
% 216.65/216.94 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 216.65/216.94 inference(quant_inst,[status(thm)],[])).
% 216.65/216.94 tff(157,plain,
% 216.65/216.94 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_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 = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))),
% 216.65/216.94 inference(modus_ponens,[status(thm)],[156, 155])).
% 216.65/216.94 tff(158,plain,
% 216.65/216.94 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))),
% 216.65/216.94 inference(unit_resolution,[status(thm)],[157, 27, 26, 25, 24, 23, 147])).
% 216.65/216.94 tff(159,plain,
% 216.65/216.94 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 216.65/216.94 inference(bind,[status(th)],[])).
% 216.65/216.94 tff(160,plain,
% 216.65/216.94 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.94 inference(quant_intro,[status(thm)],[159])).
% 216.65/216.94 tff(161,plain,
% 216.65/216.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 216.65/216.94 inference(bind,[status(th)],[])).
% 216.65/216.94 tff(162,plain,
% 216.65/216.94 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.94 inference(quant_intro,[status(thm)],[161])).
% 216.65/216.94 tff(163,plain,
% 216.65/216.94 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 216.65/216.94 inference(rewrite,[status(thm)],[])).
% 216.65/216.94 tff(164,plain,
% 216.65/216.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 216.65/216.94 inference(bind,[status(th)],[])).
% 216.65/216.94 tff(165,plain,
% 216.65/216.94 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 216.65/216.94 inference(quant_intro,[status(thm)],[164])).
% 216.65/216.94 tff(166,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_autgroup')).
% 216.65/216.94 tff(167,plain,
% 216.65/216.94 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 216.65/216.94 inference(modus_ponens,[status(thm)],[166, 165])).
% 216.65/216.94 tff(168,plain,
% 216.65/216.94 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 216.65/216.94 inference(modus_ponens,[status(thm)],[167, 163])).
% 216.65/216.94 tff(169,plain,(
% 216.65/216.94 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 216.65/216.95 inference(skolemize,[status(sab)],[168])).
% 216.65/216.95 tff(170,plain,
% 216.65/216.95 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.95 inference(modus_ponens,[status(thm)],[169, 162])).
% 216.65/216.95 tff(171,plain,
% 216.65/216.95 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 216.65/216.95 inference(modus_ponens,[status(thm)],[170, 160])).
% 216.65/216.95 tff(172,plain,
% 216.65/216.95 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 216.65/216.95 inference(rewrite,[status(thm)],[])).
% 216.65/216.95 tff(173,plain,
% 216.65/216.95 ((v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 216.65/216.95 inference(rewrite,[status(thm)],[])).
% 216.65/216.95 tff(174,plain,
% 216.65/216.95 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 216.65/216.95 inference(monotonicity,[status(thm)],[173])).
% 216.65/216.95 tff(175,plain,
% 216.65/216.95 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 216.65/216.95 inference(transitivity,[status(thm)],[174, 172])).
% 216.65/216.95 tff(176,plain,
% 216.65/216.95 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 216.65/216.95 inference(quant_inst,[status(thm)],[])).
% 216.65/216.95 tff(177,plain,
% 216.65/216.95 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.95 inference(modus_ponens,[status(thm)],[176, 175])).
% 216.65/216.95 tff(178,plain,
% 216.65/216.95 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.95 inference(unit_resolution,[status(thm)],[177, 27, 26, 25, 24, 23, 171])).
% 216.65/216.95 tff(179,plain,
% 216.65/216.95 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))),
% 216.65/216.95 inference(rewrite,[status(thm)],[])).
% 216.65/216.95 tff(180,plain,
% 216.65/216.95 (((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0))))))))))))) <=> ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))),
% 216.65/216.95 inference(rewrite,[status(thm)],[])).
% 216.65/216.95 tff(181,plain,
% 216.65/216.95 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))))))),
% 216.65/216.95 inference(monotonicity,[status(thm)],[180])).
% 216.65/216.95 tff(182,plain,
% 216.65/216.95 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))),
% 216.65/216.95 inference(transitivity,[status(thm)],[181, 179])).
% 216.65/216.95 tff(183,plain,
% 216.65/216.95 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))))))))))),
% 216.65/216.95 inference(quant_inst,[status(thm)],[])).
% 216.65/216.95 tff(184,plain,
% 216.65/216.95 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))))),
% 216.65/216.95 inference(modus_ponens,[status(thm)],[183, 182])).
% 216.65/216.95 tff(185,plain,
% 216.65/216.95 (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))),
% 216.65/216.95 inference(unit_resolution,[status(thm)],[184, 178, 158])).
% 216.65/216.95 tff(186,plain,
% 216.65/216.95 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 216.65/216.95 inference(tautology,[status(thm)],[])).
% 216.65/216.95 tff(187,plain,
% 216.65/216.95 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 216.65/216.95 inference(unit_resolution,[status(thm)],[186, 185])).
% 216.65/216.95 tff(188,plain,
% 216.65/216.95 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 216.65/216.95 inference(rewrite,[status(thm)],[])).
% 216.65/216.95 tff(189,plain,
% 216.65/216.95 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(190,plain,
% 216.65/216.96 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[189, 188])).
% 216.65/216.96 tff(191,plain,
% 216.65/216.96 (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[190, 187, 125])).
% 216.65/216.96 tff(192,plain,
% 216.65/216.96 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(193,plain,
% 216.65/216.96 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[192, 191])).
% 216.65/216.96 tff(194,plain,
% 216.65/216.96 ((~(m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(195,plain,
% 216.65/216.96 ((~(m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[194, 193])).
% 216.65/216.96 tff(196,plain,
% 216.65/216.96 (m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[195, 75])).
% 216.65/216.96 tff(197,plain,
% 216.65/216.96 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(198,plain,
% 216.65/216.96 (v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[197, 191])).
% 216.65/216.96 tff(199,plain,
% 216.65/216.96 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, B!1))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(200,plain,
% 216.65/216.96 (v1_funct_1(k6_autgroup(A!0, B!1))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[199, 191])).
% 216.65/216.96 tff(201,plain,
% 216.65/216.96 (^[A: $i, B: $i] : refl((m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(202,plain,
% 216.65/216.96 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[201])).
% 216.65/216.96 tff(203,plain,
% 216.65/216.96 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(204,plain,
% 216.65/216.96 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[203])).
% 216.65/216.96 tff(205,plain,
% 216.65/216.96 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(206,plain,
% 216.65/216.96 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(207,plain,
% 216.65/216.96 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[206])).
% 216.65/216.96 tff(208,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_group_1')).
% 216.65/216.96 tff(209,plain,
% 216.65/216.96 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[208, 207])).
% 216.65/216.96 tff(210,plain,
% 216.65/216.96 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[209, 205])).
% 216.65/216.96 tff(211,plain,(
% 216.65/216.96 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 216.65/216.96 inference(skolemize,[status(sab)],[210])).
% 216.65/216.96 tff(212,plain,
% 216.65/216.96 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[211, 204])).
% 216.65/216.96 tff(213,plain,
% 216.65/216.96 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[212, 202])).
% 216.65/216.96 tff(214,plain,
% 216.65/216.96 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(215,plain,
% 216.65/216.96 ((m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(216,plain,
% 216.65/216.96 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 216.65/216.96 inference(monotonicity,[status(thm)],[215])).
% 216.65/216.96 tff(217,plain,
% 216.65/216.96 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 216.65/216.96 inference(transitivity,[status(thm)],[216, 214])).
% 216.65/216.96 tff(218,plain,
% 216.65/216.96 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(219,plain,
% 216.65/216.96 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[218, 217])).
% 216.65/216.96 tff(220,plain,
% 216.65/216.96 (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[219, 27, 25, 24, 23, 62, 213])).
% 216.65/216.96 tff(221,plain,
% 216.65/216.96 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(222,plain,
% 216.65/216.96 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(223,plain,
% 216.65/216.96 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))))),
% 216.65/216.96 inference(monotonicity,[status(thm)],[222])).
% 216.65/216.96 tff(224,plain,
% 216.65/216.96 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 216.65/216.96 inference(transitivity,[status(thm)],[223, 221])).
% 216.65/216.96 tff(225,plain,
% 216.65/216.96 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(226,plain,
% 216.65/216.96 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[225, 224])).
% 216.65/216.96 tff(227,plain,
% 216.65/216.96 (m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[226, 27, 26, 25, 24, 23, 88, 220])).
% 216.65/216.96 tff(228,plain,
% 216.65/216.96 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(229,plain,
% 216.65/216.96 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(230,plain,
% 216.65/216.96 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[229, 228])).
% 216.65/216.96 tff(231,plain,
% 216.65/216.96 (m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[230, 121, 227])).
% 216.65/216.96 tff(232,plain,
% 216.65/216.96 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(233,plain,
% 216.65/216.96 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(234,plain,
% 216.65/216.96 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[233, 232])).
% 216.65/216.96 tff(235,plain,
% 216.65/216.96 (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[234, 187, 231])).
% 216.65/216.96 tff(236,plain,
% 216.65/216.96 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(237,plain,
% 216.65/216.96 (v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[236, 235])).
% 216.65/216.96 tff(238,plain,
% 216.65/216.96 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(239,plain,
% 216.65/216.96 (v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[238, 235])).
% 216.65/216.96 tff(240,plain,
% 216.65/216.96 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(241,plain,
% 216.65/216.96 (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[240, 73])).
% 216.65/216.96 tff(242,plain,
% 216.65/216.96 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, k3_group_1(A!0, B!1)), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(243,plain,
% 216.65/216.96 (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[242, 235])).
% 216.65/216.96 tff(244,plain,
% 216.65/216.96 ((~(m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(tautology,[status(thm)],[])).
% 216.65/216.96 tff(245,plain,
% 216.65/216.96 ((~(m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[244, 243])).
% 216.65/216.96 tff(246,plain,
% 216.65/216.96 (m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[245, 241])).
% 216.65/216.96 tff(247,plain,
% 216.65/216.96 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(248,plain,
% 216.65/216.96 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[247])).
% 216.65/216.96 tff(249,plain,
% 216.65/216.96 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(250,plain,
% 216.65/216.96 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(251,plain,
% 216.65/216.96 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[250])).
% 216.65/216.96 tff(252,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 216.65/216.96 tff(253,plain,
% 216.65/216.96 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[252, 251])).
% 216.65/216.96 tff(254,plain,
% 216.65/216.96 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[253, 249])).
% 216.65/216.96 tff(255,plain,(
% 216.65/216.96 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(skolemize,[status(sab)],[254])).
% 216.65/216.96 tff(256,plain,
% 216.65/216.96 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[255, 248])).
% 216.65/216.96 tff(257,plain,
% 216.65/216.96 (((~![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)))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(258,plain,
% 216.65/216.96 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(259,plain,
% 216.65/216.96 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[258, 257])).
% 216.65/216.96 tff(260,plain,
% 216.65/216.96 (l1_struct_0(A!0)),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[259, 23, 256])).
% 216.65/216.96 tff(261,plain,
% 216.65/216.96 (^[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))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(262,plain,
% 216.65/216.96 (![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)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[261])).
% 216.65/216.96 tff(263,plain,
% 216.65/216.96 (^[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)))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(264,plain,
% 216.65/216.96 (![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)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[263])).
% 216.65/216.96 tff(265,plain,
% 216.65/216.96 (![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))))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(266,plain,
% 216.65/216.96 (^[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)))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(267,plain,
% 216.65/216.96 (![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))))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[266])).
% 216.65/216.96 tff(268,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')).
% 216.65/216.96 tff(269,plain,
% 216.65/216.96 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[268, 267])).
% 216.65/216.96 tff(270,plain,
% 216.65/216.96 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[269, 265])).
% 216.65/216.96 tff(271,plain,(
% 216.65/216.96 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 216.65/216.96 inference(skolemize,[status(sab)],[270])).
% 216.65/216.96 tff(272,plain,
% 216.65/216.96 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[271, 264])).
% 216.65/216.96 tff(273,plain,
% 216.65/216.96 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[272, 262])).
% 216.65/216.96 tff(274,plain,
% 216.65/216.96 (((~![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))))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(275,plain,
% 216.65/216.96 ((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))))),
% 216.65/216.96 inference(rewrite,[status(thm)],[])).
% 216.65/216.96 tff(276,plain,
% 216.65/216.96 (((~![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)))))),
% 216.65/216.96 inference(monotonicity,[status(thm)],[275])).
% 216.65/216.96 tff(277,plain,
% 216.65/216.96 (((~![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))))),
% 216.65/216.96 inference(transitivity,[status(thm)],[276, 274])).
% 216.65/216.96 tff(278,plain,
% 216.65/216.96 ((~![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)))),
% 216.65/216.96 inference(quant_inst,[status(thm)],[])).
% 216.65/216.96 tff(279,plain,
% 216.65/216.96 ((~![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)))),
% 216.65/216.96 inference(modus_ponens,[status(thm)],[278, 277])).
% 216.65/216.96 tff(280,plain,
% 216.65/216.96 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[279, 27, 273])).
% 216.65/216.96 tff(281,plain,
% 216.65/216.96 (~v1_xboole_0(u1_struct_0(A!0))),
% 216.65/216.96 inference(unit_resolution,[status(thm)],[280, 260])).
% 216.65/216.96 tff(282,plain,
% 216.65/216.96 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(283,plain,
% 216.65/216.96 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 216.65/216.96 inference(quant_intro,[status(thm)],[282])).
% 216.65/216.96 tff(284,plain,
% 216.65/216.96 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))))),
% 216.65/216.96 inference(bind,[status(th)],[])).
% 216.65/216.96 tff(285,plain,
% 216.65/216.96 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[284])).
% 216.65/216.97 tff(286,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(287,plain,
% 216.65/216.97 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 216.65/216.97 inference(bind,[status(th)],[])).
% 216.65/216.97 tff(288,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[287])).
% 216.65/216.97 tff(289,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_funct_2')).
% 216.65/216.97 tff(290,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[289, 288])).
% 216.65/216.97 tff(291,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[290, 286])).
% 216.65/216.97 tff(292,plain,(
% 216.65/216.97 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 216.65/216.97 inference(skolemize,[status(sab)],[291])).
% 216.65/216.97 tff(293,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[292, 285])).
% 216.65/216.97 tff(294,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[293, 283])).
% 216.65/216.97 tff(295,plain,
% 216.65/216.97 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(296,plain,
% 216.65/216.97 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(297,plain,
% 216.65/216.97 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))))),
% 216.65/216.97 inference(monotonicity,[status(thm)],[296])).
% 216.65/216.97 tff(298,plain,
% 216.65/216.97 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 216.65/216.97 inference(transitivity,[status(thm)],[297, 295])).
% 216.65/216.97 tff(299,plain,
% 216.65/216.97 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 216.65/216.97 inference(quant_inst,[status(thm)],[])).
% 216.65/216.97 tff(300,plain,
% 216.65/216.97 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~m1_relset_1(E, B, C)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[299, 298])).
% 216.65/216.97 tff(301,plain,
% 216.65/216.97 ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))),
% 216.65/216.97 inference(unit_resolution,[status(thm)],[300, 294, 281])).
% 216.65/216.97 tff(302,plain,
% 216.65/216.97 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 216.65/216.97 inference(unit_resolution,[status(thm)],[301, 246, 239, 237, 200, 198, 196])).
% 216.65/216.97 tff(303,plain,
% 216.65/216.97 (k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 216.65/216.97 inference(symmetry,[status(thm)],[302])).
% 216.65/216.97 tff(304,plain,
% 216.65/216.97 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl(((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))),
% 216.65/216.97 inference(bind,[status(th)],[])).
% 216.65/216.97 tff(305,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[304])).
% 216.65/216.97 tff(306,plain,
% 216.65/216.97 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)) <=> (~((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) <=> (~(~((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))))), rewrite((~(~((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))) <=> ((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) <=> ((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), (((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> (((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite((((~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), (((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))))),
% 216.65/216.97 inference(bind,[status(th)],[])).
% 216.65/216.97 tff(307,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[306])).
% 216.65/216.97 tff(308,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(309,plain,
% 216.65/216.97 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) <=> (v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F))), ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) <=> ((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F)) & m1_relset_1(F, C, D)))), rewrite(((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F)) & m1_relset_1(F, C, D)) <=> (v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))), ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) <=> (v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)))), (((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite(((v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))), (((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))))),
% 216.65/216.97 inference(bind,[status(th)],[])).
% 216.65/216.97 tff(310,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[309])).
% 216.65/216.97 tff(311,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((v1_funct_1(E) & m1_relset_1(E, A, B)) & v1_funct_1(F)) & m1_relset_1(F, C, D)) => (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_partfun1')).
% 216.65/216.97 tff(312,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[311, 310])).
% 216.65/216.97 tff(313,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[312, 308])).
% 216.65/216.97 tff(314,plain,(
% 216.65/216.97 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(v1_funct_1(E) & m1_relset_1(E, A, B) & v1_funct_1(F) & m1_relset_1(F, C, D))) | (k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 216.65/216.97 inference(skolemize,[status(sab)],[313])).
% 216.65/216.97 tff(315,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[314, 307])).
% 216.65/216.97 tff(316,plain,
% 216.65/216.97 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[315, 305])).
% 216.65/216.97 tff(317,plain,
% 216.65/216.97 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(318,plain,
% 216.65/216.97 (((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(319,plain,
% 216.65/216.97 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))))),
% 216.65/216.97 inference(monotonicity,[status(thm)],[318])).
% 216.65/216.97 tff(320,plain,
% 216.65/216.97 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))))),
% 216.65/216.97 inference(transitivity,[status(thm)],[319, 317])).
% 216.65/216.97 tff(321,plain,
% 216.65/216.97 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 216.65/216.97 inference(quant_inst,[status(thm)],[])).
% 216.65/216.97 tff(322,plain,
% 216.65/216.97 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k1_partfun1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~v1_funct_1(F)) | (~v1_funct_1(E)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[321, 320])).
% 216.65/216.97 tff(323,plain,
% 216.65/216.97 (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k5_relat_1(k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 216.65/216.97 inference(unit_resolution,[status(thm)],[322, 316, 200, 239, 246, 196])).
% 216.65/216.97 tff(324,plain,
% 216.65/216.97 (k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))),
% 216.65/216.97 inference(transitivity,[status(thm)],[323, 303, 66, 34])).
% 216.65/216.97 tff(325,assumption,(u1_struct_0(A!0) = k1_xboole_0), introduced(assumption)).
% 216.65/216.97 tff(326,plain,
% 216.65/216.97 (v1_xboole_0(u1_struct_0(A!0)) <=> v1_xboole_0(k1_xboole_0)),
% 216.65/216.97 inference(monotonicity,[status(thm)],[325])).
% 216.65/216.97 tff(327,plain,
% 216.65/216.97 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(u1_struct_0(A!0))),
% 216.65/216.97 inference(symmetry,[status(thm)],[326])).
% 216.65/216.97 tff(328,plain,
% 216.65/216.97 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 216.65/216.97 inference(rewrite,[status(thm)],[])).
% 216.65/216.97 tff(329,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 216.65/216.97 tff(330,plain,
% 216.65/216.97 (v1_xboole_0(k1_xboole_0)),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[329, 328])).
% 216.65/216.97 tff(331,plain,
% 216.65/216.97 (v1_xboole_0(u1_struct_0(A!0))),
% 216.65/216.97 inference(modus_ponens,[status(thm)],[330, 327])).
% 216.65/216.97 tff(332,plain,
% 216.65/216.97 ($false),
% 216.65/216.97 inference(unit_resolution,[status(thm)],[281, 331])).
% 216.65/216.97 tff(333,plain,(~(u1_struct_0(A!0) = k1_xboole_0)), inference(lemma,lemma(discharge,[]))).
% 216.65/216.97 tff(334,plain,
% 216.65/216.97 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))))),
% 216.65/216.97 inference(bind,[status(th)],[])).
% 216.65/216.97 tff(335,plain,
% 216.65/216.97 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[334])).
% 216.65/216.97 tff(336,plain,
% 216.65/216.97 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))))),
% 216.65/216.97 inference(bind,[status(th)],[])).
% 216.65/216.97 tff(337,plain,
% 216.65/216.97 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.97 inference(quant_intro,[status(thm)],[336])).
% 216.65/216.98 tff(338,plain,
% 216.65/216.98 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.98 inference(transitivity,[status(thm)],[337, 335])).
% 216.65/216.98 tff(339,plain,
% 216.65/216.98 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))), (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(340,plain,
% 216.65/216.98 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[339])).
% 216.65/216.98 tff(341,plain,
% 216.65/216.98 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(342,plain,
% 216.65/216.98 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(343,plain,
% 216.65/216.98 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[342])).
% 216.65/216.98 tff(344,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l9_autgroup')).
% 216.65/216.98 tff(345,plain,
% 216.65/216.98 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[344, 343])).
% 216.65/216.98 tff(346,plain,
% 216.65/216.98 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[345, 341])).
% 216.65/216.98 tff(347,plain,(
% 216.65/216.98 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ((k1_relat_1(B) = k2_relat_1(B)) & (k1_relat_1(B) = u1_struct_0(A)))))),
% 216.65/216.98 inference(skolemize,[status(sab)],[346])).
% 216.65/216.98 tff(348,plain,
% 216.65/216.98 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[347, 340])).
% 216.65/216.98 tff(349,plain,
% 216.65/216.98 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[348, 338])).
% 216.65/216.98 tff(350,plain,
% 216.65/216.98 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(351,plain,
% 216.65/216.98 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(352,plain,
% 216.65/216.98 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))))),
% 216.65/216.98 inference(monotonicity,[status(thm)],[351])).
% 216.65/216.98 tff(353,plain,
% 216.65/216.98 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))),
% 216.65/216.98 inference(transitivity,[status(thm)],[352, 350])).
% 216.65/216.98 tff(354,plain,
% 216.65/216.98 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0)))))))),
% 216.65/216.98 inference(quant_inst,[status(thm)],[])).
% 216.65/216.98 tff(355,plain,
% 216.65/216.98 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[354, 353])).
% 216.65/216.98 tff(356,plain,
% 216.65/216.98 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))),
% 216.65/216.98 inference(unit_resolution,[status(thm)],[355, 27, 26, 25, 24, 23, 349])).
% 216.65/216.98 tff(357,plain,
% 216.65/216.98 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(358,plain,
% 216.65/216.98 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))))),
% 216.65/216.98 inference(quant_inst,[status(thm)],[])).
% 216.65/216.98 tff(359,plain,
% 216.65/216.98 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(B) = k2_relat_1(B))) | (~(k1_relat_1(B) = u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[358, 357])).
% 216.65/216.98 tff(360,plain,
% 216.65/216.98 (~((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))))),
% 216.65/216.98 inference(unit_resolution,[status(thm)],[359, 356, 125])).
% 216.65/216.98 tff(361,plain,
% 216.65/216.98 (((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)))) | (k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))),
% 216.65/216.98 inference(tautology,[status(thm)],[])).
% 216.65/216.98 tff(362,plain,
% 216.65/216.98 (k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)),
% 216.65/216.98 inference(unit_resolution,[status(thm)],[361, 360])).
% 216.65/216.98 tff(363,plain,
% 216.65/216.98 (((~(k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))) | (~(k1_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)))) | (k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1)))),
% 216.65/216.98 inference(tautology,[status(thm)],[])).
% 216.65/216.98 tff(364,plain,
% 216.65/216.98 (k1_relat_1(k6_autgroup(A!0, B!1)) = k2_relat_1(k6_autgroup(A!0, B!1))),
% 216.65/216.98 inference(unit_resolution,[status(thm)],[363, 360])).
% 216.65/216.98 tff(365,plain,
% 216.65/216.98 (k2_relat_1(k6_autgroup(A!0, B!1)) = k1_relat_1(k6_autgroup(A!0, B!1))),
% 216.65/216.98 inference(symmetry,[status(thm)],[364])).
% 216.65/216.98 tff(366,plain,
% 216.65/216.98 (k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0)),
% 216.65/216.98 inference(transitivity,[status(thm)],[365, 362])).
% 216.65/216.98 tff(367,plain,
% 216.65/216.98 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(368,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[367])).
% 216.65/216.98 tff(369,plain,
% 216.65/216.98 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(370,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[369])).
% 216.65/216.98 tff(371,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 216.65/216.98 inference(transitivity,[status(thm)],[370, 368])).
% 216.65/216.98 tff(372,plain,
% 216.65/216.98 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) <=> (~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> (~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))))), rewrite((~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)) <=> (~((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))), ((~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) <=> (~(~((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))))), rewrite((~(~((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))) <=> ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)))), ((~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) <=> ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))))), trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), ((~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))), ((~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), (((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))) | ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))), rewrite(((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | ((~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C))) | ((~v1_funct_1(D)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))), (((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))), (![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))) <=> ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> (((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))))), rewrite((((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(373,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[372])).
% 216.65/216.98 tff(374,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(375,plain,
% 216.65/216.98 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) <=> (v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))), trans(monotonicity(rewrite((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) <=> ((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))), trans(monotonicity(rewrite(((A = k1_xboole_0) | (B = k1_xboole_0)) <=> ((B = k1_xboole_0) | (A = k1_xboole_0))), ((((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))) <=> (((B = k1_xboole_0) | (A = k1_xboole_0)) | (D = k2_funct_1(C))))), rewrite((((B = k1_xboole_0) | (A = k1_xboole_0)) | (D = k2_funct_1(C))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)))), ((((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C))))), (((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))) <=> (((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)))))), rewrite((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))))), (((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C)))))), ((((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))) <=> ((v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)) => ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))), ((((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))) <=> ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))) <=> ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(376,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[375])).
% 216.65/216.98 tff(377,axiom,(![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, B, A)) & m2_relset_1(D, B, A)) => ((((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) & v2_funct_1(C)) => (((A = k1_xboole_0) | (B = k1_xboole_0)) | (D = k2_funct_1(C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_funct_2')).
% 216.65/216.98 tff(378,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[377, 376])).
% 216.65/216.98 tff(379,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[378, 374])).
% 216.65/216.98 tff(380,plain,(
% 216.65/216.98 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~((k2_relat_1(C) = B) & (k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A)) & v2_funct_1(C))) | (~(v1_funct_1(D) & v1_funct_2(D, B, A) & m2_relset_1(D, B, A)))))),
% 216.65/216.98 inference(skolemize,[status(sab)],[379])).
% 216.65/216.98 tff(381,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[380, 373])).
% 216.65/216.98 tff(382,plain,
% 216.65/216.98 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))),
% 216.65/216.98 inference(modus_ponens,[status(thm)],[381, 371])).
% 216.65/216.98 tff(383,plain,
% 216.65/216.98 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(384,plain,
% 216.65/216.98 (((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.65/216.98 inference(rewrite,[status(thm)],[])).
% 216.65/216.98 tff(385,plain,
% 216.65/216.98 (^[D: $i] : rewrite(((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.65/216.98 inference(bind,[status(th)],[])).
% 216.65/216.98 tff(386,plain,
% 216.65/216.98 (![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.65/216.98 inference(quant_intro,[status(thm)],[385])).
% 216.65/216.98 tff(387,plain,
% 216.65/216.98 (((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.65/216.99 inference(monotonicity,[status(thm)],[386])).
% 216.65/216.99 tff(388,plain,
% 216.65/216.99 (((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.65/216.99 inference(transitivity,[status(thm)],[387, 384])).
% 216.65/216.99 tff(389,plain,
% 216.65/216.99 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))))),
% 216.65/216.99 inference(monotonicity,[status(thm)],[388])).
% 216.65/216.99 tff(390,plain,
% 216.65/216.99 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.65/216.99 inference(transitivity,[status(thm)],[389, 383])).
% 216.65/216.99 tff(391,plain,
% 216.65/216.99 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | ((~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((u1_struct_0(A!0) = k1_xboole_0) | (u1_struct_0(A!0) = k1_xboole_0) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(D)) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 216.65/216.99 inference(quant_inst,[status(thm)],[])).
% 216.65/216.99 tff(392,plain,
% 216.65/216.99 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((B = k1_xboole_0) | (A = k1_xboole_0) | (D = k2_funct_1(C)) | (~v1_funct_1(D)) | (~(k2_relat_1(C) = B)) | (~(k1_partfun1(A, B, B, A, C, D) = k6_partfun1(A))) | (~v2_funct_1(C)) | (~v1_funct_2(D, B, A)) | (~m2_relset_1(D, B, A))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.65/216.99 inference(modus_ponens,[status(thm)],[391, 390])).
% 216.65/216.99 tff(393,plain,
% 216.65/216.99 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.65/216.99 inference(unit_resolution,[status(thm)],[392, 382, 200, 198, 193])).
% 216.65/216.99 tff(394,plain,
% 216.65/216.99 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)),
% 216.65/216.99 inference(tautology,[status(thm)],[])).
% 216.65/216.99 tff(395,plain,
% 216.65/216.99 (v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)),
% 216.65/216.99 inference(unit_resolution,[status(thm)],[394, 191])).
% 216.65/216.99 tff(396,plain,
% 216.65/216.99 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))),
% 216.65/216.99 inference(tautology,[status(thm)],[])).
% 216.65/216.99 tff(397,plain,
% 216.65/216.99 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))),
% 216.65/216.99 inference(unit_resolution,[status(thm)],[396, 185])).
% 216.65/216.99 tff(398,plain,
% 216.65/216.99 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))))),
% 216.65/216.99 inference(rewrite,[status(thm)],[])).
% 216.65/216.99 tff(399,plain,
% 216.65/216.99 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))))),
% 216.65/216.99 inference(quant_inst,[status(thm)],[])).
% 216.65/216.99 tff(400,plain,
% 216.65/216.99 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k6_autgroup(A!0, B!1), A!0, A!0)) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))),
% 216.65/216.99 inference(modus_ponens,[status(thm)],[399, 398])).
% 216.65/216.99 tff(401,plain,
% 216.65/216.99 (~(((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 216.65/216.99 inference(unit_resolution,[status(thm)],[400, 200, 397, 198, 395, 193])).
% 216.65/216.99 tff(402,plain,
% 216.65/216.99 (^[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))))),
% 216.65/216.99 inference(bind,[status(th)],[])).
% 216.65/216.99 tff(403,plain,
% 216.65/216.99 (![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)))),
% 216.65/216.99 inference(quant_intro,[status(thm)],[402])).
% 216.65/216.99 tff(404,plain,
% 216.65/216.99 (^[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))))),
% 216.65/216.99 inference(bind,[status(th)],[])).
% 216.65/216.99 tff(405,plain,
% 216.65/216.99 (![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)))),
% 216.65/216.99 inference(quant_intro,[status(thm)],[404])).
% 216.65/216.99 tff(406,plain,
% 216.65/216.99 (^[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))))),
% 216.65/216.99 inference(bind,[status(th)],[])).
% 216.65/216.99 tff(407,plain,
% 216.65/216.99 (![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)))),
% 216.65/216.99 inference(quant_intro,[status(thm)],[406])).
% 216.65/216.99 tff(408,plain,
% 216.65/216.99 (![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)))),
% 216.65/216.99 inference(transitivity,[status(thm)],[407, 405])).
% 216.65/216.99 tff(409,plain,
% 216.65/216.99 (^[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)))))),
% 216.65/216.99 inference(bind,[status(th)],[])).
% 216.65/216.99 tff(410,plain,
% 216.65/216.99 (![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)))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[409])).
% 216.75/216.99 tff(411,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(412,plain,
% 216.75/216.99 (^[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))))),
% 216.75/216.99 inference(bind,[status(th)],[])).
% 216.75/216.99 tff(413,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[412])).
% 216.75/216.99 tff(414,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')).
% 216.75/216.99 tff(415,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[414, 413])).
% 216.75/216.99 tff(416,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[415, 411])).
% 216.75/216.99 tff(417,plain,(
% 216.75/216.99 ![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)))),
% 216.75/216.99 inference(skolemize,[status(sab)],[416])).
% 216.75/216.99 tff(418,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[417, 410])).
% 216.75/216.99 tff(419,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[418, 408])).
% 216.75/216.99 tff(420,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[419, 403])).
% 216.75/216.99 tff(421,plain,
% 216.75/216.99 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(422,plain,
% 216.75/216.99 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 216.75/216.99 inference(quant_inst,[status(thm)],[])).
% 216.75/216.99 tff(423,plain,
% 216.75/216.99 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[422, 421])).
% 216.75/216.99 tff(424,plain,
% 216.75/216.99 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[423, 420, 281, 178])).
% 216.75/216.99 tff(425,plain,
% 216.75/216.99 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 216.75/216.99 inference(quant_inst,[status(thm)],[])).
% 216.75/216.99 tff(426,plain,
% 216.75/216.99 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[425, 424])).
% 216.75/216.99 tff(427,plain,
% 216.75/216.99 ((~(m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 216.75/216.99 inference(tautology,[status(thm)],[])).
% 216.75/216.99 tff(428,plain,
% 216.75/216.99 ((~(m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) | m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[427, 125])).
% 216.75/216.99 tff(429,plain,
% 216.75/216.99 (m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[428, 426])).
% 216.75/216.99 tff(430,plain,
% 216.75/216.99 (^[A: $i, B: $i, C: $i] : refl(((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 216.75/216.99 inference(bind,[status(th)],[])).
% 216.75/216.99 tff(431,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[430])).
% 216.75/216.99 tff(432,plain,
% 216.75/216.99 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 216.75/216.99 inference(bind,[status(th)],[])).
% 216.75/216.99 tff(433,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[432])).
% 216.75/216.99 tff(434,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(435,plain,
% 216.75/216.99 (^[A: $i, B: $i, C: $i] : rewrite((m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))))),
% 216.75/216.99 inference(bind,[status(th)],[])).
% 216.75/216.99 tff(436,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[435])).
% 216.75/216.99 tff(437,axiom,(![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_fraenkel')).
% 216.75/216.99 tff(438,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[437, 436])).
% 216.75/216.99 tff(439,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[438, 434])).
% 216.75/216.99 tff(440,plain,(
% 216.75/216.99 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 216.75/216.99 inference(skolemize,[status(sab)],[439])).
% 216.75/216.99 tff(441,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[440, 433])).
% 216.75/216.99 tff(442,plain,
% 216.75/216.99 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[441, 431])).
% 216.75/216.99 tff(443,plain,
% 216.75/216.99 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(444,plain,
% 216.75/216.99 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 216.75/216.99 inference(quant_inst,[status(thm)],[])).
% 216.75/216.99 tff(445,plain,
% 216.75/216.99 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[444, 443])).
% 216.75/216.99 tff(446,plain,
% 216.75/216.99 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[445, 442, 178])).
% 216.75/216.99 tff(447,plain,
% 216.75/216.99 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 216.75/216.99 inference(tautology,[status(thm)],[])).
% 216.75/216.99 tff(448,plain,
% 216.75/216.99 (~v1_xboole_0(k1_autgroup(A!0))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[447, 446])).
% 216.75/216.99 tff(449,plain,
% 216.75/216.99 (^[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))))),
% 216.75/216.99 inference(bind,[status(th)],[])).
% 216.75/216.99 tff(450,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[449])).
% 216.75/216.99 tff(451,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(452,plain,
% 216.75/216.99 (^[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))))),
% 216.75/216.99 inference(bind,[status(th)],[])).
% 216.75/216.99 tff(453,plain,
% 216.75/216.99 (![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)))),
% 216.75/216.99 inference(quant_intro,[status(thm)],[452])).
% 216.75/216.99 tff(454,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')).
% 216.75/216.99 tff(455,plain,
% 216.75/216.99 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[454, 453])).
% 216.75/216.99 tff(456,plain,
% 216.75/216.99 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[455, 451])).
% 216.75/216.99 tff(457,plain,(
% 216.75/216.99 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 216.75/216.99 inference(skolemize,[status(sab)],[456])).
% 216.75/216.99 tff(458,plain,
% 216.75/216.99 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[457, 450])).
% 216.75/216.99 tff(459,plain,
% 216.75/216.99 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(460,plain,
% 216.75/216.99 ((r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))) <=> (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 216.75/216.99 inference(rewrite,[status(thm)],[])).
% 216.75/216.99 tff(461,plain,
% 216.75/216.99 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))),
% 216.75/216.99 inference(monotonicity,[status(thm)],[460])).
% 216.75/216.99 tff(462,plain,
% 216.75/216.99 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 216.75/216.99 inference(transitivity,[status(thm)],[461, 459])).
% 216.75/216.99 tff(463,plain,
% 216.75/216.99 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))))),
% 216.75/216.99 inference(quant_inst,[status(thm)],[])).
% 216.75/216.99 tff(464,plain,
% 216.75/216.99 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 216.75/216.99 inference(modus_ponens,[status(thm)],[463, 462])).
% 216.75/216.99 tff(465,plain,
% 216.75/216.99 (r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[464, 458, 448, 429])).
% 216.75/216.99 tff(466,plain,
% 216.75/216.99 ((((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0)))) | (~r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0)))),
% 216.75/216.99 inference(tautology,[status(thm)],[])).
% 216.75/216.99 tff(467,plain,
% 216.75/216.99 ((((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) <=> r2_hidden(k6_autgroup(A!0, B!1), k1_autgroup(A!0))) | (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))))),
% 216.75/216.99 inference(unit_resolution,[status(thm)],[466, 465])).
% 216.75/217.00 tff(468,plain,
% 216.75/217.00 (~((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0)))),
% 216.75/217.00 inference(unit_resolution,[status(thm)],[467, 401])).
% 216.75/217.00 tff(469,plain,
% 216.75/217.00 (((~v2_funct_1(k6_autgroup(A!0, B!1))) | (~v3_group_6(k6_autgroup(A!0, B!1), A!0, A!0))) | v2_funct_1(k6_autgroup(A!0, B!1))),
% 216.75/217.00 inference(tautology,[status(thm)],[])).
% 216.75/217.00 tff(470,plain,
% 216.75/217.00 (v2_funct_1(k6_autgroup(A!0, B!1))),
% 216.75/217.00 inference(unit_resolution,[status(thm)],[469, 468])).
% 216.75/217.00 tff(471,plain,
% 216.75/217.00 (~(k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1)))),
% 216.75/217.00 inference(or_elim,[status(thm)],[61])).
% 216.75/217.00 tff(472,plain,
% 216.75/217.00 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.75/217.00 inference(rewrite,[status(thm)],[])).
% 216.75/217.00 tff(473,plain,
% 216.75/217.00 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))) <=> ((k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.75/217.00 inference(rewrite,[status(thm)],[])).
% 216.75/217.00 tff(474,plain,
% 216.75/217.00 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))))),
% 216.75/217.00 inference(monotonicity,[status(thm)],[473])).
% 216.75/217.00 tff(475,plain,
% 216.75/217.00 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.75/217.06 inference(transitivity,[status(thm)],[474, 472])).
% 216.75/217.06 tff(476,plain,
% 216.75/217.06 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))))),
% 216.75/217.06 inference(quant_inst,[status(thm)],[])).
% 216.75/217.06 tff(477,plain,
% 216.75/217.06 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (D = k2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k6_partfun1(u1_struct_0(A!0)))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k2_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v2_funct_1(k6_autgroup(A!0, B!1))) | (~(k2_relat_1(k6_autgroup(A!0, B!1)) = u1_struct_0(A!0))) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))),
% 216.75/217.06 inference(modus_ponens,[status(thm)],[476, 475])).
% 216.75/217.06 tff(478,plain,
% 216.75/217.06 ((u1_struct_0(A!0) = k1_xboole_0) | (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0))))),
% 216.75/217.06 inference(unit_resolution,[status(thm)],[477, 471, 239, 237, 243, 470, 393, 366])).
% 216.75/217.06 tff(479,plain,
% 216.75/217.06 (~(k1_partfun1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k6_autgroup(A!0, k3_group_1(A!0, B!1))) = k6_partfun1(u1_struct_0(A!0)))),
% 216.75/217.06 inference(unit_resolution,[status(thm)],[478, 333])).
% 216.75/217.06 tff(480,plain,
% 216.75/217.06 ($false),
% 216.75/217.06 inference(unit_resolution,[status(thm)],[479, 324])).
% 216.75/217.06 % SZS output end Proof
% 216.88/217.13 % E exiting
%------------------------------------------------------------------------------