%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP640+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:16 AM UTC 2025
% Result : Theorem 30.33s 30.52s
% Output : Proof 30.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP640+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:35:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 30.33/30.52 % SZS status Theorem
% 30.33/30.52 % SZS output start Proof
% 30.33/30.52 tff(k2_funct_2_type, type, (
% 30.33/30.52 k2_funct_2: ( $i * $i * $i * $i ) > $i)).
% 30.33/30.52 tff(u1_struct_0_type, type, (
% 30.33/30.52 u1_struct_0: $i > $i)).
% 30.33/30.52 tff(k5_group_4_type, type, (
% 30.33/30.52 k5_group_4: ( $i * $i ) > $i)).
% 30.33/30.52 tff(k2_xboole_0_type, type, (
% 30.33/30.52 k2_xboole_0: ( $i * $i ) > $i)).
% 30.33/30.52 tff(tptp_fun_D_3_type, type, (
% 30.33/30.52 tptp_fun_D_3: $i)).
% 30.33/30.52 tff(tptp_fun_C_2_type, type, (
% 30.33/30.52 tptp_fun_C_2: $i)).
% 30.33/30.52 tff(tptp_fun_A_0_type, type, (
% 30.33/30.52 tptp_fun_A_0: $i)).
% 30.33/30.52 tff(tptp_fun_E_4_type, type, (
% 30.33/30.52 tptp_fun_E_4: $i)).
% 30.33/30.52 tff(tptp_fun_B_1_type, type, (
% 30.33/30.52 tptp_fun_B_1: $i)).
% 30.33/30.52 tff(k8_group_4_type, type, (
% 30.33/30.52 k8_group_4: ( $i * $i * $i ) > $i)).
% 30.33/30.52 tff(u1_group_1_type, type, (
% 30.33/30.52 u1_group_1: $i > $i)).
% 30.33/30.52 tff(g1_group_1_type, type, (
% 30.33/30.52 g1_group_1: ( $i * $i ) > $i)).
% 30.33/30.52 tff(r1_group_2_type, type, (
% 30.33/30.52 r1_group_2: ( $i * $i * $i ) > $o)).
% 30.33/30.52 tff(v1_group_1_type, type, (
% 30.33/30.52 v1_group_1: $i > $o)).
% 30.33/30.52 tff(m1_group_2_type, type, (
% 30.33/30.52 m1_group_2: ( $i * $i ) > $o)).
% 30.33/30.52 tff(m1_subset_1_type, type, (
% 30.33/30.52 m1_subset_1: ( $i * $i ) > $o)).
% 30.33/30.52 tff(k1_zfmisc_1_type, type, (
% 30.33/30.52 k1_zfmisc_1: $i > $i)).
% 30.33/30.52 tff(l1_group_1_type, type, (
% 30.33/30.52 l1_group_1: $i > $o)).
% 30.33/30.52 tff(v4_group_1_type, type, (
% 30.33/30.52 v4_group_1: $i > $o)).
% 30.33/30.52 tff(v3_group_1_type, type, (
% 30.33/30.52 v3_group_1: $i > $o)).
% 30.33/30.52 tff(v3_struct_0_type, type, (
% 30.33/30.52 v3_struct_0: $i > $o)).
% 30.33/30.52 tff(m2_relset_1_type, type, (
% 30.33/30.52 m2_relset_1: ( $i * $i * $i ) > $o)).
% 30.33/30.52 tff(v1_funct_2_type, type, (
% 30.33/30.52 v1_funct_2: ( $i * $i * $i ) > $o)).
% 30.33/30.52 tff(v1_funct_1_type, type, (
% 30.33/30.52 v1_funct_1: $i > $o)).
% 30.33/30.52 tff(m1_relset_1_type, type, (
% 30.33/30.52 m1_relset_1: ( $i * $i * $i ) > $o)).
% 30.33/30.52 tff(k2_zfmisc_1_type, type, (
% 30.33/30.52 k2_zfmisc_1: ( $i * $i ) > $i)).
% 30.33/30.52 tff(1,plain,
% 30.33/30.52 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))))),
% 30.33/30.52 inference(bind,[status(th)],[])).
% 30.33/30.52 tff(2,plain,
% 30.33/30.52 (![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), 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, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 30.33/30.52 inference(quant_intro,[status(thm)],[1])).
% 30.33/30.52 tff(3,plain,
% 30.33/30.52 (^[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, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(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, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)) <=> (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))))),
% 30.33/30.52 inference(bind,[status(th)],[])).
% 30.33/30.52 tff(4,plain,
% 30.33/30.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), 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, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 30.33/30.52 inference(quant_intro,[status(thm)],[3])).
% 30.33/30.52 tff(5,plain,
% 30.33/30.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), 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, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 30.33/30.52 inference(rewrite,[status(thm)],[])).
% 30.33/30.52 tff(6,plain,
% 30.33/30.52 (^[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, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(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, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))))),
% 30.33/30.52 inference(bind,[status(th)],[])).
% 30.33/30.52 tff(7,plain,
% 30.33/30.52 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), 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, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 30.33/30.52 inference(quant_intro,[status(thm)],[6])).
% 30.33/30.52 tff(8,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, k1_zfmisc_1(u1_struct_0(A)))) => (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_group_4')).
% 30.33/30.52 tff(9,plain,
% 30.33/30.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 30.33/30.52 inference(modus_ponens,[status(thm)],[8, 7])).
% 30.33/30.52 tff(10,plain,
% 30.33/30.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 30.33/30.52 inference(modus_ponens,[status(thm)],[9, 5])).
% 30.33/30.52 tff(11,plain,(
% 30.33/30.52 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (v1_group_1(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)))),
% 30.33/30.52 inference(skolemize,[status(sab)],[10])).
% 30.33/30.52 tff(12,plain,
% 30.33/30.52 (![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 30.33/30.52 inference(modus_ponens,[status(thm)],[11, 4])).
% 30.33/30.52 tff(13,plain,
% 30.33/30.52 (![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))),
% 30.33/30.52 inference(modus_ponens,[status(thm)],[12, 2])).
% 30.33/30.52 tff(14,plain,
% 30.33/30.52 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.52 inference(rewrite,[status(thm)],[])).
% 30.33/30.52 tff(15,plain,
% 30.33/30.52 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.52 inference(rewrite,[status(thm)],[])).
% 30.33/30.52 tff(16,plain,
% 30.33/30.52 ((m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> (m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.52 inference(rewrite,[status(thm)],[])).
% 30.33/30.52 tff(17,plain,
% 30.33/30.52 ((~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 30.33/30.52 inference(rewrite,[status(thm)],[])).
% 30.33/30.52 tff(18,plain,
% 30.33/30.52 ((m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.52 inference(monotonicity,[status(thm)],[17])).
% 30.33/30.52 tff(19,plain,
% 30.33/30.52 ((m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> (m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))))),
% 30.33/30.52 inference(monotonicity,[status(thm)],[18])).
% 30.33/30.52 tff(20,plain,
% 30.33/30.52 ((m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> (m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.52 inference(transitivity,[status(thm)],[19, 16])).
% 30.33/30.52 tff(21,plain,
% 30.33/30.52 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))))) <=> (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))))),
% 30.33/30.52 inference(monotonicity,[status(thm)],[20])).
% 30.33/30.52 tff(22,plain,
% 30.33/30.52 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.53 inference(transitivity,[status(thm)],[21, 15])).
% 30.33/30.53 tff(23,plain,
% 30.33/30.53 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))))),
% 30.33/30.53 inference(monotonicity,[status(thm)],[22])).
% 30.33/30.53 tff(24,plain,
% 30.33/30.53 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (m1_group_2(C!2, A!0) & (m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 30.33/30.53 inference(transitivity,[status(thm)],[23, 14])).
% 30.33/30.53 tff(25,plain,
% 30.33/30.53 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B)))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B))))))))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(26,plain,
% 30.33/30.53 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_group_2(D, A) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B))) => ![F: $i] : (m1_subset_1(F, k1_zfmisc_1(u1_struct_0(A))) => ((F = k2_xboole_0(u1_struct_0(C), u1_struct_0(D))) => (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, F)))))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B))))))))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(27,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_group_2(D, A) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B))) => ![F: $i] : (m1_subset_1(F, k1_zfmisc_1(u1_struct_0(A))) => ((F = k2_xboole_0(u1_struct_0(C), u1_struct_0(D))) => (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, F)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t13_latsubgr')).
% 30.33/30.53 tff(28,plain,
% 30.33/30.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B)))))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[27, 26])).
% 30.33/30.53 tff(29,plain,
% 30.33/30.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B)))))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[28, 25])).
% 30.33/30.53 tff(30,plain,
% 30.33/30.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B)))))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[29, 25])).
% 30.33/30.53 tff(31,plain,
% 30.33/30.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m1_group_2(C, A)) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(C), u1_struct_0(D)), k1_zfmisc_1(u1_struct_0(A)))) | (k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k8_group_4(A, C, D))) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), E, u1_struct_0(k5_group_4(A, k2_xboole_0(u1_struct_0(C), u1_struct_0(D)))))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(E, u1_struct_0(A), u1_struct_0(B)))))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[30, 25])).
% 30.33/30.53 tff(32,plain,
% 30.33/30.53 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & m1_group_2(C!2, A!0) & m1_group_2(D!3, A!0) & (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[31, 24])).
% 30.33/30.53 tff(33,plain,
% 30.33/30.53 (~((~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(v1_funct_1(E!4) & v1_funct_2(E!4, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(E!4, u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 30.33/30.53 inference(and_elim,[status(thm)],[32])).
% 30.33/30.53 tff(34,plain,
% 30.33/30.53 (m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 30.33/30.53 inference(or_elim,[status(thm)],[33])).
% 30.33/30.53 tff(35,plain,
% 30.33/30.53 (l1_group_1(A!0)),
% 30.33/30.53 inference(and_elim,[status(thm)],[32])).
% 30.33/30.53 tff(36,plain,
% 30.33/30.53 (v4_group_1(A!0)),
% 30.33/30.53 inference(and_elim,[status(thm)],[32])).
% 30.33/30.53 tff(37,plain,
% 30.33/30.53 (v3_group_1(A!0)),
% 30.33/30.53 inference(and_elim,[status(thm)],[32])).
% 30.33/30.53 tff(38,plain,
% 30.33/30.53 (~v3_struct_0(A!0)),
% 30.33/30.53 inference(and_elim,[status(thm)],[32])).
% 30.33/30.53 tff(39,plain,
% 30.33/30.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(40,plain,
% 30.33/30.53 ((v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(41,plain,
% 30.33/30.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0))))))),
% 30.33/30.53 inference(monotonicity,[status(thm)],[40])).
% 30.33/30.53 tff(42,plain,
% 30.33/30.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))),
% 30.33/30.53 inference(transitivity,[status(thm)],[41, 39])).
% 30.33/30.53 tff(43,plain,
% 30.33/30.53 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))))),
% 30.33/30.53 inference(quant_inst,[status(thm)],[])).
% 30.33/30.53 tff(44,plain,
% 30.33/30.53 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~v1_group_1(k5_group_4(A, B))) | (~m1_group_2(k5_group_4(A, B), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[43, 42])).
% 30.33/30.53 tff(45,plain,
% 30.33/30.53 (~((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[44, 38, 37, 36, 35, 34, 13])).
% 30.33/30.53 tff(46,plain,
% 30.33/30.53 (((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0))) | v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.33/30.53 inference(tautology,[status(thm)],[])).
% 30.33/30.53 tff(47,plain,
% 30.33/30.53 (v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[46, 45])).
% 30.33/30.53 tff(48,plain,
% 30.33/30.53 (((~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0))) | m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)),
% 30.33/30.53 inference(tautology,[status(thm)],[])).
% 30.33/30.53 tff(49,plain,
% 30.33/30.53 (m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[48, 45])).
% 30.33/30.53 tff(50,plain,
% 30.33/30.53 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(51,plain,
% 30.33/30.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[50])).
% 30.33/30.53 tff(52,plain,
% 30.33/30.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(53,plain,
% 30.33/30.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[52])).
% 30.33/30.53 tff(54,plain,
% 30.33/30.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(transitivity,[status(thm)],[53, 51])).
% 30.33/30.53 tff(55,plain,
% 30.33/30.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(56,plain,
% 30.33/30.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[55])).
% 30.33/30.53 tff(57,plain,
% 30.33/30.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(58,plain,
% 30.33/30.53 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(59,plain,
% 30.33/30.53 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[58])).
% 30.33/30.53 tff(60,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_group_2')).
% 30.33/30.53 tff(61,plain,
% 30.33/30.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[60, 59])).
% 30.33/30.53 tff(62,plain,
% 30.33/30.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[61, 57])).
% 30.33/30.53 tff(63,plain,(
% 30.33/30.53 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 30.33/30.53 inference(skolemize,[status(sab)],[62])).
% 30.33/30.53 tff(64,plain,
% 30.33/30.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[63, 56])).
% 30.33/30.53 tff(65,plain,
% 30.33/30.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[64, 54])).
% 30.33/30.53 tff(66,plain,
% 30.33/30.53 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(67,plain,
% 30.33/30.53 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 30.33/30.53 inference(quant_inst,[status(thm)],[])).
% 30.33/30.53 tff(68,plain,
% 30.33/30.53 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[67, 66])).
% 30.33/30.53 tff(69,plain,
% 30.33/30.53 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[68, 38, 37, 35, 65])).
% 30.33/30.53 tff(70,plain,
% 30.33/30.53 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)) | (~(v3_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v3_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)) | (~(v3_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v3_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(71,plain,
% 30.33/30.53 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)) | (~(v3_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v3_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))),
% 30.33/30.53 inference(quant_inst,[status(thm)],[])).
% 30.33/30.53 tff(72,plain,
% 30.33/30.53 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)) | (~(v3_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v3_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[71, 70])).
% 30.33/30.53 tff(73,plain,
% 30.33/30.53 (~(v3_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v3_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[72, 69, 49])).
% 30.33/30.53 tff(74,plain,
% 30.33/30.53 ((v3_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v3_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.33/30.53 inference(tautology,[status(thm)],[])).
% 30.33/30.53 tff(75,plain,
% 30.33/30.53 (l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[74, 73])).
% 30.33/30.53 tff(76,plain,
% 30.33/30.53 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(77,plain,
% 30.33/30.53 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[76])).
% 30.33/30.53 tff(78,plain,
% 30.33/30.53 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(79,plain,
% 30.33/30.53 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(80,plain,
% 30.33/30.53 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[79])).
% 30.33/30.53 tff(81,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 30.33/30.53 tff(82,plain,
% 30.33/30.53 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[81, 80])).
% 30.33/30.53 tff(83,plain,
% 30.33/30.53 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[82, 78])).
% 30.33/30.53 tff(84,plain,(
% 30.33/30.53 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(skolemize,[status(sab)],[83])).
% 30.33/30.53 tff(85,plain,
% 30.33/30.53 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[84, 77])).
% 30.33/30.53 tff(86,plain,
% 30.33/30.53 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(87,plain,
% 30.33/30.53 (((k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> ((~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))),
% 30.33/30.53 inference(rewrite,[status(thm)],[])).
% 30.33/30.53 tff(88,plain,
% 30.33/30.53 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))),
% 30.33/30.53 inference(monotonicity,[status(thm)],[87])).
% 30.33/30.53 tff(89,plain,
% 30.33/30.53 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))),
% 30.33/30.53 inference(transitivity,[status(thm)],[88, 86])).
% 30.33/30.53 tff(90,plain,
% 30.33/30.53 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.33/30.53 inference(quant_inst,[status(thm)],[])).
% 30.33/30.53 tff(91,plain,
% 30.33/30.53 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.33/30.53 inference(modus_ponens,[status(thm)],[90, 89])).
% 30.33/30.53 tff(92,plain,
% 30.33/30.53 ((~l1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (~v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) | (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[91, 85])).
% 30.33/30.53 tff(93,plain,
% 30.33/30.53 (k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))),
% 30.33/30.53 inference(unit_resolution,[status(thm)],[92, 75, 47])).
% 30.33/30.53 tff(94,plain,
% 30.33/30.53 (g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))) = k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))),
% 30.33/30.53 inference(symmetry,[status(thm)],[93])).
% 30.33/30.53 tff(95,plain,
% 30.33/30.53 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A))))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(96,plain,
% 30.33/30.53 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[95])).
% 30.33/30.53 tff(97,plain,
% 30.33/30.53 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A))))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A))))), rewrite((v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)) <=> (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> ((v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A))) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A))) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))))),
% 30.33/30.53 inference(bind,[status(th)],[])).
% 30.33/30.53 tff(98,plain,
% 30.33/30.53 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))),
% 30.33/30.53 inference(quant_intro,[status(thm)],[97])).
% 30.33/30.53 tff(99,plain,
% 30.33/30.53 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))),
% 30.33/30.54 inference(rewrite,[status(thm)],[])).
% 30.33/30.54 tff(100,plain,
% 30.33/30.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(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_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))))),
% 30.33/30.54 inference(bind,[status(th)],[])).
% 30.33/30.54 tff(101,plain,
% 30.33/30.54 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))),
% 30.33/30.54 inference(quant_intro,[status(thm)],[100])).
% 30.33/30.54 tff(102,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_group_4')).
% 30.33/30.54 tff(103,plain,
% 30.33/30.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[102, 101])).
% 30.33/30.54 tff(104,plain,
% 30.33/30.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[103, 99])).
% 30.33/30.54 tff(105,plain,(
% 30.33/30.54 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)))),
% 30.33/30.54 inference(skolemize,[status(sab)],[104])).
% 30.33/30.54 tff(106,plain,
% 30.33/30.54 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[105, 98])).
% 30.33/30.54 tff(107,plain,
% 30.33/30.54 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[106, 96])).
% 30.33/30.54 tff(108,plain,
% 30.33/30.54 (m1_group_2(D!3, A!0)),
% 30.33/30.54 inference(and_elim,[status(thm)],[32])).
% 30.33/30.54 tff(109,plain,
% 30.33/30.54 (m1_group_2(C!2, A!0)),
% 30.33/30.54 inference(and_elim,[status(thm)],[32])).
% 30.33/30.54 tff(110,plain,
% 30.33/30.54 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_group_2(C!2, A!0)) | (~m1_group_2(D!3, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | v3_struct_0(A!0) | (~m1_group_2(C!2, A!0)) | (~m1_group_2(D!3, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))),
% 30.33/30.54 inference(rewrite,[status(thm)],[])).
% 30.33/30.54 tff(111,plain,
% 30.33/30.54 ((v3_struct_0(A!0) | (~m1_group_2(D!3, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0))))) <=> (v3_struct_0(A!0) | (~m1_group_2(C!2, A!0)) | (~m1_group_2(D!3, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))),
% 30.33/30.54 inference(rewrite,[status(thm)],[])).
% 30.33/30.54 tff(112,plain,
% 30.33/30.54 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_group_2(D!3, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_group_2(C!2, A!0)) | (~m1_group_2(D!3, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0))))))),
% 30.33/30.54 inference(monotonicity,[status(thm)],[111])).
% 30.33/30.54 tff(113,plain,
% 30.33/30.54 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_group_2(D!3, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | v3_struct_0(A!0) | (~m1_group_2(C!2, A!0)) | (~m1_group_2(D!3, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))),
% 30.33/30.54 inference(transitivity,[status(thm)],[112, 110])).
% 30.33/30.54 tff(114,plain,
% 30.33/30.54 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_group_2(D!3, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))))),
% 30.33/30.54 inference(quant_inst,[status(thm)],[])).
% 30.33/30.54 tff(115,plain,
% 30.33/30.54 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~((~v1_group_1(k8_group_4(A, B, C))) | (~m1_group_2(k8_group_4(A, B, C), A)))))) | v3_struct_0(A!0) | (~m1_group_2(C!2, A!0)) | (~m1_group_2(D!3, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0))))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[114, 113])).
% 30.33/30.54 tff(116,plain,
% 30.33/30.54 (~((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)))),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[115, 38, 37, 36, 35, 109, 108, 107])).
% 30.33/30.54 tff(117,plain,
% 30.33/30.54 (((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0))) | v1_group_1(k8_group_4(A!0, C!2, D!3))),
% 30.33/30.54 inference(tautology,[status(thm)],[])).
% 30.33/30.54 tff(118,plain,
% 30.33/30.54 (v1_group_1(k8_group_4(A!0, C!2, D!3))),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[117, 116])).
% 30.33/30.54 tff(119,plain,
% 30.33/30.54 (((~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0))) | m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)),
% 30.33/30.54 inference(tautology,[status(thm)],[])).
% 30.33/30.54 tff(120,plain,
% 30.33/30.54 (m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[119, 116])).
% 30.33/30.54 tff(121,plain,
% 30.33/30.54 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)) | (~(v3_struct_0(k8_group_4(A!0, C!2, D!3)) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v3_group_1(k8_group_4(A!0, C!2, D!3))))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)) | (~(v3_struct_0(k8_group_4(A!0, C!2, D!3)) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v3_group_1(k8_group_4(A!0, C!2, D!3))))))),
% 30.33/30.54 inference(rewrite,[status(thm)],[])).
% 30.33/30.54 tff(122,plain,
% 30.33/30.54 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)) | (~(v3_struct_0(k8_group_4(A!0, C!2, D!3)) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v3_group_1(k8_group_4(A!0, C!2, D!3))))))),
% 30.33/30.54 inference(quant_inst,[status(thm)],[])).
% 30.33/30.54 tff(123,plain,
% 30.33/30.54 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)) | (~(v3_struct_0(k8_group_4(A!0, C!2, D!3)) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v3_group_1(k8_group_4(A!0, C!2, D!3)))))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[122, 121])).
% 30.33/30.54 tff(124,plain,
% 30.33/30.54 (~(v3_struct_0(k8_group_4(A!0, C!2, D!3)) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v3_group_1(k8_group_4(A!0, C!2, D!3))))),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[123, 69, 120])).
% 30.33/30.54 tff(125,plain,
% 30.33/30.54 ((v3_struct_0(k8_group_4(A!0, C!2, D!3)) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v3_group_1(k8_group_4(A!0, C!2, D!3)))) | l1_group_1(k8_group_4(A!0, C!2, D!3))),
% 30.33/30.54 inference(tautology,[status(thm)],[])).
% 30.33/30.54 tff(126,plain,
% 30.33/30.54 (l1_group_1(k8_group_4(A!0, C!2, D!3))),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[125, 124])).
% 30.33/30.54 tff(127,plain,
% 30.33/30.54 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))),
% 30.33/30.54 inference(rewrite,[status(thm)],[])).
% 30.33/30.54 tff(128,plain,
% 30.33/30.54 (((k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3)))) <=> ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))),
% 30.33/30.54 inference(rewrite,[status(thm)],[])).
% 30.33/30.54 tff(129,plain,
% 30.33/30.54 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))))),
% 30.33/30.54 inference(monotonicity,[status(thm)],[128])).
% 30.33/30.54 tff(130,plain,
% 30.33/30.54 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))),
% 30.33/30.54 inference(transitivity,[status(thm)],[129, 127])).
% 30.33/30.54 tff(131,plain,
% 30.33/30.54 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))))),
% 30.33/30.54 inference(quant_inst,[status(thm)],[])).
% 30.33/30.54 tff(132,plain,
% 30.33/30.54 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))),
% 30.33/30.54 inference(modus_ponens,[status(thm)],[131, 130])).
% 30.33/30.54 tff(133,plain,
% 30.33/30.54 ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~v1_group_1(k8_group_4(A!0, C!2, D!3))) | (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[132, 85])).
% 30.33/30.54 tff(134,plain,
% 30.33/30.54 (k8_group_4(A!0, C!2, D!3) = g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))),
% 30.33/30.54 inference(unit_resolution,[status(thm)],[133, 126, 118])).
% 30.33/30.54 tff(135,plain,
% 30.33/30.54 (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = k8_group_4(A!0, C!2, D!3)),
% 30.33/30.54 inference(symmetry,[status(thm)],[134])).
% 30.33/30.54 tff(136,plain,
% 30.33/30.54 (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.33/30.54 inference(monotonicity,[status(thm)],[135, 94])).
% 30.33/30.54 tff(137,plain,
% 30.33/30.54 (r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) <=> r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.33/30.54 inference(symmetry,[status(thm)],[136])).
% 30.33/30.54 tff(138,plain,
% 30.33/30.54 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))))),
% 30.33/30.54 inference(bind,[status(th)],[])).
% 30.33/30.54 tff(139,plain,
% 30.33/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.33/30.54 inference(quant_intro,[status(thm)],[138])).
% 30.33/30.54 tff(140,plain,
% 30.33/30.54 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 30.33/30.54 inference(bind,[status(th)],[])).
% 30.33/30.54 tff(141,plain,
% 30.33/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 30.33/30.54 inference(quant_intro,[status(thm)],[140])).
% 30.33/30.54 tff(142,plain,
% 30.33/30.54 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 30.33/30.54 inference(bind,[status(th)],[])).
% 30.33/30.54 tff(143,plain,
% 30.33/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 30.33/30.54 inference(quant_intro,[status(thm)],[142])).
% 30.33/30.54 tff(144,plain,
% 30.33/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 30.33/30.54 inference(transitivity,[status(thm)],[143, 141])).
% 30.33/30.54 tff(145,plain,
% 30.33/30.54 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 30.40/30.54 inference(bind,[status(th)],[])).
% 30.40/30.54 tff(146,plain,
% 30.40/30.54 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 30.40/30.54 inference(quant_intro,[status(thm)],[145])).
% 30.40/30.54 tff(147,plain,
% 30.40/30.54 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.54 inference(rewrite,[status(thm)],[])).
% 30.40/30.54 tff(148,plain,
% 30.40/30.54 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))) <=> ((~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))) <=> (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))))), rewrite((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))) <=> (r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)) | (~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))) <=> (r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)) | (~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))) <=> ![D: $i] : (r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)) | (~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), trans(der(![D: $i] : (r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)) | (~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) <=> ![D: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))), elim_unused(![D: $i] : ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))) <=> ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))), (![D: $i] : (r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)) | (~(D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))) <=> ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))), ((m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))))) <=> (m1_group_2(C, A) => ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))), rewrite((m1_group_2(C, A) => ((~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) <=> ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))), ((m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))))) <=> ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))), (![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))))) <=> ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))), ((m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))))) <=> (m1_group_2(B, A) => ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))), rewrite((m1_group_2(B, A) => ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) <=> ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))), ((m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))))) <=> ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))))), (![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))))),
% 30.40/30.54 inference(bind,[status(th)],[])).
% 30.40/30.54 tff(149,plain,
% 30.40/30.54 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.54 inference(quant_intro,[status(thm)],[148])).
% 30.40/30.54 tff(150,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = k2_xboole_0(u1_struct_0(B), u1_struct_0(C))) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, D)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_latsubgr')).
% 30.40/30.54 tff(151,plain,
% 30.40/30.54 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.54 inference(modus_ponens,[status(thm)],[150, 149])).
% 30.40/30.54 tff(152,plain,
% 30.40/30.54 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.54 inference(modus_ponens,[status(thm)],[151, 147])).
% 30.40/30.54 tff(153,plain,(
% 30.40/30.54 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.54 inference(skolemize,[status(sab)],[152])).
% 30.40/30.54 tff(154,plain,
% 30.40/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 30.40/30.54 inference(modus_ponens,[status(thm)],[153, 146])).
% 30.40/30.54 tff(155,plain,
% 30.40/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 30.40/30.54 inference(modus_ponens,[status(thm)],[154, 144])).
% 30.40/30.54 tff(156,plain,
% 30.40/30.54 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.54 inference(modus_ponens,[status(thm)],[155, 139])).
% 30.40/30.54 tff(157,plain,
% 30.40/30.54 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.55 inference(rewrite,[status(thm)],[])).
% 30.40/30.55 tff(158,plain,
% 30.40/30.55 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))),
% 30.40/30.55 inference(quant_inst,[status(thm)],[])).
% 30.40/30.55 tff(159,plain,
% 30.40/30.55 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : ((~m1_group_2(C, A)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A)))) | r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k2_xboole_0(u1_struct_0(B), u1_struct_0(C)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[158, 157])).
% 30.40/30.55 tff(160,plain,
% 30.40/30.55 (![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))),
% 30.40/30.55 inference(unit_resolution,[status(thm)],[159, 38, 37, 36, 35, 156])).
% 30.40/30.55 tff(161,plain,
% 30.40/30.55 (((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) | ((~m1_group_2(C!2, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C))))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C))))))),
% 30.40/30.55 inference(rewrite,[status(thm)],[])).
% 30.40/30.55 tff(162,plain,
% 30.40/30.55 ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) | ((~m1_group_2(C!2, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C))))))),
% 30.40/30.55 inference(quant_inst,[status(thm)],[])).
% 30.40/30.55 tff(163,plain,
% 30.40/30.55 ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(B), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, B, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(B), u1_struct_0(C))))))) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)))))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[162, 161])).
% 30.40/30.55 tff(164,plain,
% 30.40/30.55 (![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)))))),
% 30.40/30.55 inference(unit_resolution,[status(thm)],[163, 109, 160])).
% 30.40/30.55 tff(165,plain,
% 30.40/30.55 (((~![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)))))) | ((~m1_group_2(D!3, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> ((~![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)))))) | (~m1_group_2(D!3, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))),
% 30.40/30.55 inference(rewrite,[status(thm)],[])).
% 30.40/30.55 tff(166,plain,
% 30.40/30.55 ((~![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)))))) | ((~m1_group_2(D!3, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))),
% 30.40/30.55 inference(quant_inst,[status(thm)],[])).
% 30.40/30.55 tff(167,plain,
% 30.40/30.55 ((~![C: $i] : ((~m1_group_2(C, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, C), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(C)))))) | (~m1_group_2(D!3, A!0)) | (~m1_subset_1(k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[166, 165])).
% 30.40/30.55 tff(168,plain,
% 30.40/30.55 (r1_group_2(A!0, k8_group_4(A!0, C!2, D!3), k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.40/30.55 inference(unit_resolution,[status(thm)],[167, 108, 34, 164])).
% 30.40/30.55 tff(169,plain,
% 30.40/30.55 (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[168, 137])).
% 30.40/30.55 tff(170,plain,
% 30.40/30.55 (v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))) <=> v1_group_1(k8_group_4(A!0, C!2, D!3))),
% 30.40/30.55 inference(monotonicity,[status(thm)],[135])).
% 30.40/30.55 tff(171,plain,
% 30.40/30.55 (v1_group_1(k8_group_4(A!0, C!2, D!3)) <=> v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))),
% 30.40/30.55 inference(symmetry,[status(thm)],[170])).
% 30.40/30.55 tff(172,plain,
% 30.40/30.55 (v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[118, 171])).
% 30.40/30.55 tff(173,plain,
% 30.40/30.55 (v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.40/30.55 inference(monotonicity,[status(thm)],[94])).
% 30.40/30.55 tff(174,plain,
% 30.40/30.55 (v1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))) <=> v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.40/30.55 inference(symmetry,[status(thm)],[173])).
% 30.40/30.55 tff(175,plain,
% 30.40/30.55 (v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[47, 174])).
% 30.40/30.55 tff(176,plain,
% 30.40/30.55 (m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0) <=> m1_group_2(k8_group_4(A!0, C!2, D!3), A!0)),
% 30.40/30.55 inference(monotonicity,[status(thm)],[135])).
% 30.40/30.55 tff(177,plain,
% 30.40/30.55 (m1_group_2(k8_group_4(A!0, C!2, D!3), A!0) <=> m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)),
% 30.40/30.55 inference(symmetry,[status(thm)],[176])).
% 30.40/30.55 tff(178,plain,
% 30.40/30.55 (m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[120, 177])).
% 30.40/30.55 tff(179,plain,
% 30.40/30.55 (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0) <=> m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0)),
% 30.40/30.55 inference(monotonicity,[status(thm)],[94])).
% 30.40/30.55 tff(180,plain,
% 30.40/30.55 (m1_group_2(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))), A!0) <=> m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)),
% 30.40/30.55 inference(symmetry,[status(thm)],[179])).
% 30.40/30.55 tff(181,plain,
% 30.40/30.55 (m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[49, 180])).
% 30.40/30.55 tff(182,plain,
% 30.40/30.55 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))) <=> (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))))),
% 30.40/30.55 inference(bind,[status(th)],[])).
% 30.40/30.55 tff(183,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))),
% 30.40/30.55 inference(quant_intro,[status(thm)],[182])).
% 30.40/30.55 tff(184,plain,
% 30.40/30.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C))) <=> ((v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))) | (r1_group_2(A, B, C) <=> (B = C))))), rewrite(((v3_struct_0(A) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A))) | (r1_group_2(A, B, C) <=> (B = C))) <=> (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C))) <=> (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))))),
% 30.40/30.55 inference(bind,[status(th)],[])).
% 30.40/30.55 tff(185,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))),
% 30.40/30.55 inference(quant_intro,[status(thm)],[184])).
% 30.40/30.55 tff(186,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))),
% 30.40/30.55 inference(rewrite,[status(thm)],[])).
% 30.40/30.55 tff(187,plain,
% 30.40/30.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(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)) & v1_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & v1_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & v1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A)) & v1_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A)) & v1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C)))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) & m1_group_2(C, A)) => (r1_group_2(A, B, C) <=> (B = C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A)) => (r1_group_2(A, B, C) <=> (B = C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A)) => (r1_group_2(A, B, C) <=> (B = C))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) & m1_group_2(C, A)) => (r1_group_2(A, B, C) <=> (B = C))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))))),
% 30.40/30.55 inference(bind,[status(th)],[])).
% 30.40/30.55 tff(188,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) & m1_group_2(C, A)) => (r1_group_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))),
% 30.40/30.55 inference(quant_intro,[status(thm)],[187])).
% 30.40/30.55 tff(189,axiom,(![A: $i, B: $i, C: $i] : (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & v1_group_1(B)) & m1_group_2(B, A)) & v1_group_1(C)) & m1_group_2(C, A)) => (r1_group_2(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_group_2')).
% 30.40/30.55 tff(190,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[189, 188])).
% 30.40/30.55 tff(191,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[190, 186])).
% 30.40/30.55 tff(192,plain,(
% 30.40/30.55 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(B, A) & v1_group_1(C) & m1_group_2(C, A))) | (r1_group_2(A, B, C) <=> (B = C)))),
% 30.40/30.55 inference(skolemize,[status(sab)],[191])).
% 30.40/30.55 tff(193,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[192, 185])).
% 30.40/30.55 tff(194,plain,
% 30.40/30.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))),
% 30.40/30.55 inference(modus_ponens,[status(thm)],[193, 183])).
% 30.40/30.55 tff(195,plain,
% 30.40/30.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))))),
% 30.40/30.55 inference(rewrite,[status(thm)],[])).
% 30.40/30.55 tff(196,plain,
% 30.40/30.55 ((v3_struct_0(A!0) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))))),
% 30.40/30.55 inference(rewrite,[status(thm)],[])).
% 30.40/30.55 tff(197,plain,
% 30.40/30.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | (v3_struct_0(A!0) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))))),
% 30.40/30.55 inference(monotonicity,[status(thm)],[196])).
% 30.40/30.55 tff(198,plain,
% 30.40/30.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | (v3_struct_0(A!0) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))))),
% 30.40/30.55 inference(transitivity,[status(thm)],[197, 195])).
% 30.40/30.55 tff(199,plain,
% 30.40/30.55 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | (v3_struct_0(A!0) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))))) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)))),
% 30.40/30.55 inference(quant_inst,[status(thm)],[])).
% 30.40/30.55 tff(200,plain,
% 30.40/30.55 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r1_group_2(A, B, C) <=> (B = C)) | (~m1_group_2(C, A)) | (~v1_group_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(B)) | (~m1_group_2(B, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))), A!0)) | (~m1_group_2(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), A!0)) | (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[199, 198])).
% 30.40/30.56 tff(201,plain,
% 30.40/30.56 ((r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~v1_group_1(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3)))))),
% 30.40/30.56 inference(unit_resolution,[status(thm)],[200, 38, 37, 36, 35, 194, 181, 178])).
% 30.40/30.56 tff(202,plain,
% 30.40/30.56 (r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.40/30.56 inference(unit_resolution,[status(thm)],[201, 175, 172])).
% 30.40/30.56 tff(203,plain,
% 30.40/30.56 ((~(r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) <=> (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))) | (~r1_group_2(A!0, g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))), g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.40/30.56 inference(tautology,[status(thm)],[])).
% 30.40/30.56 tff(204,plain,
% 30.40/30.56 (g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))),
% 30.40/30.56 inference(unit_resolution,[status(thm)],[203, 202, 169])).
% 30.40/30.56 tff(205,plain,
% 30.40/30.56 (^[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)))),
% 30.40/30.56 inference(bind,[status(th)],[])).
% 30.40/30.56 tff(206,plain,
% 30.40/30.56 (![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))),
% 30.40/30.56 inference(quant_intro,[status(thm)],[205])).
% 30.40/30.56 tff(207,plain,
% 30.40/30.56 (![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))),
% 30.40/30.56 inference(rewrite,[status(thm)],[])).
% 30.40/30.56 tff(208,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 30.40/30.56 tff(209,plain,
% 30.40/30.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[208, 207])).
% 30.40/30.56 tff(210,plain,(
% 30.40/30.56 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 30.40/30.56 inference(skolemize,[status(sab)],[209])).
% 30.40/30.56 tff(211,plain,
% 30.40/30.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[210, 206])).
% 30.40/30.56 tff(212,plain,
% 30.40/30.56 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))) <=> m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))),
% 30.40/30.56 inference(quant_inst,[status(thm)],[])).
% 30.40/30.56 tff(213,plain,
% 30.40/30.56 (m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))) <=> m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.40/30.56 inference(unit_resolution,[status(thm)],[212, 211])).
% 30.40/30.56 tff(214,plain,
% 30.40/30.56 (^[A: $i] : refl(((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 30.40/30.56 inference(bind,[status(th)],[])).
% 30.40/30.56 tff(215,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 30.40/30.56 inference(quant_intro,[status(thm)],[214])).
% 30.40/30.56 tff(216,plain,
% 30.40/30.56 (^[A: $i] : rewrite(((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 30.40/30.56 inference(bind,[status(th)],[])).
% 30.40/30.56 tff(217,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 30.40/30.56 inference(quant_intro,[status(thm)],[216])).
% 30.40/30.56 tff(218,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 30.40/30.56 inference(rewrite,[status(thm)],[])).
% 30.40/30.56 tff(219,plain,
% 30.40/30.56 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_group_1(A) => (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_group_1(A) => (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 30.40/30.56 inference(bind,[status(th)],[])).
% 30.40/30.56 tff(220,plain,
% 30.40/30.56 (![A: $i] : (l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 30.40/30.56 inference(quant_intro,[status(thm)],[219])).
% 30.40/30.56 tff(221,axiom,(![A: $i] : (l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_group_1')).
% 30.40/30.56 tff(222,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[221, 220])).
% 30.40/30.56 tff(223,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[222, 218])).
% 30.40/30.56 tff(224,plain,(
% 30.40/30.56 ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 30.40/30.56 inference(skolemize,[status(sab)],[223])).
% 30.40/30.56 tff(225,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[224, 217])).
% 30.40/30.56 tff(226,plain,
% 30.40/30.56 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[225, 215])).
% 30.40/30.56 tff(227,plain,
% 30.40/30.56 (((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))))) <=> ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))))),
% 30.40/30.56 inference(rewrite,[status(thm)],[])).
% 30.40/30.56 tff(228,plain,
% 30.40/30.56 ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))))),
% 30.40/30.56 inference(quant_inst,[status(thm)],[])).
% 30.40/30.56 tff(229,plain,
% 30.40/30.56 ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))))),
% 30.40/30.56 inference(modus_ponens,[status(thm)],[228, 227])).
% 30.41/30.56 tff(230,plain,
% 30.41/30.56 ((~l1_group_1(k8_group_4(A!0, C!2, D!3))) | (~((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[229, 226])).
% 30.41/30.56 tff(231,plain,
% 30.41/30.56 (~((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[230, 126])).
% 30.41/30.56 tff(232,plain,
% 30.41/30.56 (((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))) | m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(tautology,[status(thm)],[])).
% 30.41/30.56 tff(233,plain,
% 30.41/30.56 (m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[232, 231])).
% 30.41/30.56 tff(234,plain,
% 30.41/30.56 ((~(m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))) <=> m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(tautology,[status(thm)],[])).
% 30.41/30.56 tff(235,plain,
% 30.41/30.56 ((~(m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))) <=> m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))) | m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[234, 233])).
% 30.41/30.56 tff(236,plain,
% 30.41/30.56 (m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[235, 213])).
% 30.41/30.56 tff(237,plain,
% 30.41/30.56 (((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))) | v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(tautology,[status(thm)],[])).
% 30.41/30.56 tff(238,plain,
% 30.41/30.56 (v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[237, 231])).
% 30.41/30.56 tff(239,plain,
% 30.41/30.56 (((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m2_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))) | v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(tautology,[status(thm)],[])).
% 30.41/30.56 tff(240,plain,
% 30.41/30.56 (v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))),
% 30.41/30.56 inference(unit_resolution,[status(thm)],[239, 231])).
% 30.41/30.56 tff(241,plain,
% 30.41/30.56 (^[A: $i, B: $i] : refl(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 30.41/30.56 inference(bind,[status(th)],[])).
% 30.41/30.56 tff(242,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 30.41/30.56 inference(quant_intro,[status(thm)],[241])).
% 30.41/30.56 tff(243,plain,
% 30.41/30.56 (^[A: $i, B: $i] : rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 30.41/30.56 inference(bind,[status(th)],[])).
% 30.41/30.56 tff(244,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 30.41/30.56 inference(quant_intro,[status(thm)],[243])).
% 30.41/30.56 tff(245,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 30.41/30.56 inference(transitivity,[status(thm)],[244, 242])).
% 30.41/30.56 tff(246,plain,
% 30.41/30.56 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))) <=> ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))))),
% 30.41/30.56 inference(bind,[status(th)],[])).
% 30.41/30.56 tff(247,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 30.41/30.56 inference(quant_intro,[status(thm)],[246])).
% 30.41/30.56 tff(248,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 30.41/30.56 inference(rewrite,[status(thm)],[])).
% 30.41/30.56 tff(249,plain,
% 30.41/30.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))) <=> ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))))),
% 30.41/30.56 inference(bind,[status(th)],[])).
% 30.41/30.56 tff(250,plain,
% 30.41/30.56 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 30.41/30.56 inference(quant_intro,[status(thm)],[249])).
% 30.41/30.56 tff(251,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g1_group_1')).
% 30.41/30.56 tff(252,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 30.41/30.56 inference(modus_ponens,[status(thm)],[251, 250])).
% 30.41/30.56 tff(253,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 30.41/30.56 inference(modus_ponens,[status(thm)],[252, 248])).
% 30.41/30.56 tff(254,plain,(
% 30.41/30.56 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 30.41/30.56 inference(skolemize,[status(sab)],[253])).
% 30.41/30.56 tff(255,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 30.41/30.56 inference(modus_ponens,[status(thm)],[254, 247])).
% 30.41/30.56 tff(256,plain,
% 30.41/30.56 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 30.41/30.56 inference(modus_ponens,[status(thm)],[255, 245])).
% 30.41/30.56 tff(257,plain,
% 30.41/30.56 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))),
% 30.41/30.56 inference(rewrite,[status(thm)],[])).
% 30.41/30.56 tff(258,plain,
% 30.41/30.56 (((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) <=> ((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))),
% 30.41/30.56 inference(rewrite,[status(thm)],[])).
% 30.41/30.56 tff(259,plain,
% 30.41/30.56 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))))),
% 30.41/30.56 inference(monotonicity,[status(thm)],[258])).
% 30.41/30.56 tff(260,plain,
% 30.41/30.57 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))))),
% 30.41/30.57 inference(transitivity,[status(thm)],[259, 257])).
% 30.41/30.57 tff(261,plain,
% 30.41/30.57 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))))),
% 30.41/30.57 inference(quant_inst,[status(thm)],[])).
% 30.41/30.57 tff(262,plain,
% 30.41/30.57 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(u1_group_1(k8_group_4(A!0, C!2, D!3)))) | (~v1_funct_2(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3)))) | ![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))),
% 30.41/30.57 inference(modus_ponens,[status(thm)],[261, 260])).
% 30.41/30.57 tff(263,plain,
% 30.41/30.57 (![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D))))) | (~m1_relset_1(u1_group_1(k8_group_4(A!0, C!2, D!3)), k2_zfmisc_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_struct_0(k8_group_4(A!0, C!2, D!3))), u1_struct_0(k8_group_4(A!0, C!2, D!3))))),
% 30.41/30.57 inference(unit_resolution,[status(thm)],[262, 256, 240, 238])).
% 30.41/30.57 tff(264,plain,
% 30.41/30.57 (![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))),
% 30.41/30.57 inference(unit_resolution,[status(thm)],[263, 236])).
% 30.41/30.57 tff(265,plain,
% 30.41/30.57 (((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))) <=> ((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | (~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))),
% 30.41/30.57 inference(rewrite,[status(thm)],[])).
% 30.41/30.57 tff(266,plain,
% 30.41/30.57 (((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))) <=> ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))),
% 30.41/30.57 inference(rewrite,[status(thm)],[])).
% 30.41/30.57 tff(267,plain,
% 30.41/30.57 (((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))) <=> ((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))))),
% 30.41/30.57 inference(monotonicity,[status(thm)],[266])).
% 30.41/30.57 tff(268,plain,
% 30.41/30.57 (((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))) <=> ((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | (~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))),
% 30.41/30.57 inference(transitivity,[status(thm)],[267, 265])).
% 30.41/30.57 tff(269,plain,
% 30.41/30.57 ((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))))),
% 30.41/30.57 inference(quant_inst,[status(thm)],[])).
% 30.41/30.57 tff(270,plain,
% 30.41/30.57 ((~![C: $i, D: $i] : ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(C, D))) | (~((~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = C)) | (~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = D)))))) | (~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))),
% 30.41/30.57 inference(modus_ponens,[status(thm)],[269, 268])).
% 30.41/30.57 tff(271,plain,
% 30.41/30.57 ((~(g1_group_1(u1_struct_0(k8_group_4(A!0, C!2, D!3)), u1_group_1(k8_group_4(A!0, C!2, D!3))) = g1_group_1(u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))), u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))))),
% 30.50/30.66 inference(unit_resolution,[status(thm)],[270, 264])).
% 30.50/30.66 tff(272,plain,
% 30.50/30.66 (~((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))))),
% 30.50/30.66 inference(unit_resolution,[status(thm)],[271, 204])).
% 30.50/30.66 tff(273,plain,
% 30.50/30.66 (((~(u1_group_1(k8_group_4(A!0, C!2, D!3)) = u1_group_1(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))) | (~(u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))) | (u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))),
% 30.50/30.66 inference(tautology,[status(thm)],[])).
% 30.50/30.66 tff(274,plain,
% 30.50/30.66 (u1_struct_0(k8_group_4(A!0, C!2, D!3)) = u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))),
% 30.50/30.66 inference(unit_resolution,[status(thm)],[273, 272])).
% 30.50/30.66 tff(275,plain,
% 30.50/30.66 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3)))))),
% 30.50/30.66 inference(monotonicity,[status(thm)],[274])).
% 30.50/30.66 tff(276,plain,
% 30.50/30.66 (~(k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k8_group_4(A!0, C!2, D!3))) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), E!4, u1_struct_0(k5_group_4(A!0, k2_xboole_0(u1_struct_0(C!2), u1_struct_0(D!3))))))),
% 30.50/30.66 inference(or_elim,[status(thm)],[33])).
% 30.50/30.66 tff(277,plain,
% 30.50/30.66 ($false),
% 30.50/30.66 inference(unit_resolution,[status(thm)],[276, 275])).
% 30.50/30.66 % SZS output end Proof
% 30.50/30.73 % E exiting
%------------------------------------------------------------------------------