%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP653+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:08:19 AM UTC 2025
% Result : Theorem 53.63s 53.80s
% Output : Proof 53.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP653+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:43:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 53.63/53.80 % SZS status Theorem
% 53.63/53.80 % SZS output start Proof
% 53.63/53.80 tff(m1_lattice4_type, type, (
% 53.63/53.80 m1_lattice4: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(g3_lattices_type, type, (
% 53.63/53.80 g3_lattices: ( $i * $i * $i ) > $i)).
% 53.63/53.80 tff(u1_lattices_type, type, (
% 53.63/53.80 u1_lattices: $i > $i)).
% 53.63/53.80 tff(k11_group_4_type, type, (
% 53.63/53.80 k11_group_4: $i > $i)).
% 53.63/53.80 tff(tptp_fun_B_1_type, type, (
% 53.63/53.80 tptp_fun_B_1: $i)).
% 53.63/53.80 tff(u2_lattices_type, type, (
% 53.63/53.80 u2_lattices: $i > $i)).
% 53.63/53.80 tff(u1_struct_0_type, type, (
% 53.63/53.80 u1_struct_0: $i > $i)).
% 53.63/53.80 tff(tptp_fun_A_0_type, type, (
% 53.63/53.80 tptp_fun_A_0: $i)).
% 53.63/53.80 tff(k3_latsubgr_type, type, (
% 53.63/53.80 k3_latsubgr: ( $i * $i * $i ) > $i)).
% 53.63/53.80 tff(tptp_fun_C_2_type, type, (
% 53.63/53.80 tptp_fun_C_2: $i)).
% 53.63/53.80 tff(m4_vectsp_8_type, type, (
% 53.63/53.80 m4_vectsp_8: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(m3_vectsp_8_type, type, (
% 53.63/53.80 m3_vectsp_8: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(v1_funct_2_type, type, (
% 53.63/53.80 v1_funct_2: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(l3_lattices_type, type, (
% 53.63/53.80 l3_lattices: $i > $o)).
% 53.63/53.80 tff(v10_lattices_type, type, (
% 53.63/53.80 v10_lattices: $i > $o)).
% 53.63/53.80 tff(v3_lattices_type, type, (
% 53.63/53.80 v3_lattices: $i > $o)).
% 53.63/53.80 tff(v3_struct_0_type, type, (
% 53.63/53.80 v3_struct_0: $i > $o)).
% 53.63/53.80 tff(v4_group_1_type, type, (
% 53.63/53.80 v4_group_1: $i > $o)).
% 53.63/53.80 tff(v3_group_1_type, type, (
% 53.63/53.80 v3_group_1: $i > $o)).
% 53.63/53.80 tff(l1_group_1_type, type, (
% 53.63/53.80 l1_group_1: $i > $o)).
% 53.63/53.80 tff(m2_relset_1_type, type, (
% 53.63/53.80 m2_relset_1: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(v1_group_6_type, type, (
% 53.63/53.80 v1_group_6: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(v1_funct_1_type, type, (
% 53.63/53.80 v1_funct_1: $i > $o)).
% 53.63/53.80 tff(v2_funct_1_type, type, (
% 53.63/53.80 v2_funct_1: $i > $o)).
% 53.63/53.80 tff(v15_lattices_type, type, (
% 53.63/53.80 v15_lattices: $i > $o)).
% 53.63/53.80 tff(v14_lattices_type, type, (
% 53.63/53.80 v14_lattices: $i > $o)).
% 53.63/53.80 tff(v13_lattices_type, type, (
% 53.63/53.80 v13_lattices: $i > $o)).
% 53.63/53.80 tff(v9_lattices_type, type, (
% 53.63/53.80 v9_lattices: $i > $o)).
% 53.63/53.80 tff(v8_lattices_type, type, (
% 53.63/53.80 v8_lattices: $i > $o)).
% 53.63/53.80 tff(v7_lattices_type, type, (
% 53.63/53.80 v7_lattices: $i > $o)).
% 53.63/53.80 tff(v6_lattices_type, type, (
% 53.63/53.80 v6_lattices: $i > $o)).
% 53.63/53.80 tff(v5_lattices_type, type, (
% 53.63/53.80 v5_lattices: $i > $o)).
% 53.63/53.80 tff(v4_lattices_type, type, (
% 53.63/53.80 v4_lattices: $i > $o)).
% 53.63/53.80 tff(m1_relset_1_type, type, (
% 53.63/53.80 m1_relset_1: ( $i * $i * $i ) > $o)).
% 53.63/53.80 tff(1,plain,
% 53.63/53.80 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A)))))))),
% 53.63/53.80 inference(bind,[status(th)],[])).
% 53.63/53.80 tff(2,plain,
% 53.63/53.80 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))),
% 53.63/53.80 inference(quant_intro,[status(thm)],[1])).
% 53.63/53.80 tff(3,plain,
% 53.63/53.80 (^[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))))), rewrite(((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))) <=> (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))))),
% 53.63/53.80 inference(bind,[status(th)],[])).
% 53.63/53.80 tff(4,plain,
% 53.63/53.80 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))),
% 53.63/53.80 inference(quant_intro,[status(thm)],[3])).
% 53.63/53.80 tff(5,plain,
% 53.63/53.80 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))),
% 53.63/53.80 inference(rewrite,[status(thm)],[])).
% 53.63/53.80 tff(6,plain,
% 53.63/53.80 (^[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)))), trans(monotonicity(rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)))), (((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))), (((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))))),
% 53.63/53.80 inference(bind,[status(th)],[])).
% 53.63/53.80 tff(7,plain,
% 53.63/53.80 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))),
% 53.63/53.80 inference(quant_intro,[status(thm)],[6])).
% 53.63/53.80 tff(8,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & l3_lattices(k11_group_4(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k11_group_4')).
% 53.63/53.80 tff(9,plain,
% 53.63/53.80 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))),
% 53.63/53.80 inference(modus_ponens,[status(thm)],[8, 7])).
% 53.63/53.80 tff(10,plain,
% 53.63/53.80 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))),
% 53.63/53.80 inference(modus_ponens,[status(thm)],[9, 5])).
% 53.63/53.80 tff(11,plain,(
% 53.63/53.80 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & l3_lattices(k11_group_4(A))))),
% 53.63/53.80 inference(skolemize,[status(sab)],[10])).
% 53.63/53.80 tff(12,plain,
% 53.63/53.80 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))),
% 53.63/53.80 inference(modus_ponens,[status(thm)],[11, 4])).
% 53.63/53.80 tff(13,plain,
% 53.63/53.80 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))),
% 53.63/53.80 inference(modus_ponens,[status(thm)],[12, 2])).
% 53.63/53.80 tff(14,plain,
% 53.63/53.80 ((((~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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, 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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(15,plain,
% 53.63/53.81 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (~(m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, 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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(16,plain,
% 53.63/53.81 ((~(m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (~(m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(17,plain,
% 53.63/53.81 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (~(m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, 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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 53.63/53.81 inference(monotonicity,[status(thm)],[16])).
% 53.63/53.81 tff(18,plain,
% 53.63/53.81 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (~(m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, 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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 53.63/53.81 inference(transitivity,[status(thm)],[17, 15])).
% 53.63/53.81 tff(19,plain,
% 53.63/53.81 ((((~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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, 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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))))),
% 53.63/53.81 inference(monotonicity,[status(thm)],[18])).
% 53.63/53.81 tff(20,plain,
% 53.63/53.81 ((((~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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, 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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 53.63/53.81 inference(transitivity,[status(thm)],[19, 14])).
% 53.63/53.81 tff(21,plain,
% 53.63/53.81 ((~![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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, 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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(22,plain,
% 53.63/53.81 ((~![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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m1_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(23,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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m1_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t38_latsubgr')).
% 53.63/53.81 tff(24,plain,
% 53.63/53.81 (~![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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[23, 22])).
% 53.63/53.81 tff(25,plain,
% 53.63/53.81 (~![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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[24, 21])).
% 53.63/53.81 tff(26,plain,
% 53.63/53.81 (~![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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[25, 21])).
% 53.63/53.81 tff(27,plain,
% 53.63/53.81 (~![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_lattice4(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[26, 21])).
% 53.63/53.81 tff(28,plain,
% 53.63/53.81 ((~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_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[27, 20])).
% 53.63/53.81 tff(29,plain,
% 53.63/53.81 (l1_group_1(B!1)),
% 53.63/53.81 inference(and_elim,[status(thm)],[28])).
% 53.63/53.81 tff(30,plain,
% 53.63/53.81 (v4_group_1(B!1)),
% 53.63/53.81 inference(and_elim,[status(thm)],[28])).
% 53.63/53.81 tff(31,plain,
% 53.63/53.81 (v3_group_1(B!1)),
% 53.63/53.81 inference(and_elim,[status(thm)],[28])).
% 53.63/53.81 tff(32,plain,
% 53.63/53.81 (~v3_struct_0(B!1)),
% 53.63/53.81 inference(and_elim,[status(thm)],[28])).
% 53.63/53.81 tff(33,plain,
% 53.63/53.81 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(34,plain,
% 53.63/53.81 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))))),
% 53.63/53.81 inference(quant_inst,[status(thm)],[])).
% 53.63/53.81 tff(35,plain,
% 53.63/53.81 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1)))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[34, 33])).
% 53.63/53.81 tff(36,plain,
% 53.63/53.81 (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))),
% 53.63/53.81 inference(unit_resolution,[status(thm)],[35, 32, 31, 30, 29, 13])).
% 53.63/53.81 tff(37,plain,
% 53.63/53.81 ((v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1)))) | l3_lattices(k11_group_4(B!1))),
% 53.63/53.81 inference(tautology,[status(thm)],[])).
% 53.63/53.81 tff(38,plain,
% 53.63/53.81 (l3_lattices(k11_group_4(B!1))),
% 53.63/53.81 inference(unit_resolution,[status(thm)],[37, 36])).
% 53.63/53.81 tff(39,plain,
% 53.63/53.81 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A)))))))),
% 53.63/53.81 inference(bind,[status(th)],[])).
% 53.63/53.81 tff(40,plain,
% 53.63/53.81 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))),
% 53.63/53.81 inference(quant_intro,[status(thm)],[39])).
% 53.63/53.81 tff(41,plain,
% 53.63/53.81 (^[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))))), rewrite(((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))) <=> (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))))),
% 53.63/53.81 inference(bind,[status(th)],[])).
% 53.63/53.81 tff(42,plain,
% 53.63/53.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))),
% 53.63/53.81 inference(quant_intro,[status(thm)],[41])).
% 53.63/53.81 tff(43,plain,
% 53.63/53.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(44,plain,
% 53.63/53.81 (^[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)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)))), (((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)))), (((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A))))), ((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)))), ((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A))))), (((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)))), (((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A))))), ((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)))), ((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A))))), (((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)))), (((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A))))), ((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)))), ((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A))))), (((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)))), (((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A))))), ((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)))), ((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A))))), (((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A))) <=> (((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A))))), rewrite((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))), (((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A))) <=> ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))))),
% 53.63/53.81 inference(bind,[status(th)],[])).
% 53.63/53.81 tff(45,plain,
% 53.63/53.81 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))),
% 53.63/53.81 inference(quant_intro,[status(thm)],[44])).
% 53.63/53.81 tff(46,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((((((((((((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A))) & v4_lattices(k11_group_4(A))) & v5_lattices(k11_group_4(A))) & v6_lattices(k11_group_4(A))) & v7_lattices(k11_group_4(A))) & v8_lattices(k11_group_4(A))) & v9_lattices(k11_group_4(A))) & v10_lattices(k11_group_4(A))) & v13_lattices(k11_group_4(A))) & v14_lattices(k11_group_4(A))) & v15_lattices(k11_group_4(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_group_4')).
% 53.63/53.81 tff(47,plain,
% 53.63/53.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[46, 45])).
% 53.63/53.81 tff(48,plain,
% 53.63/53.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[47, 43])).
% 53.63/53.81 tff(49,plain,(
% 53.63/53.81 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ((~v3_struct_0(k11_group_4(A))) & v3_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A))))),
% 53.63/53.81 inference(skolemize,[status(sab)],[48])).
% 53.63/53.81 tff(50,plain,
% 53.63/53.81 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[49, 42])).
% 53.63/53.81 tff(51,plain,
% 53.63/53.81 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[50, 40])).
% 53.63/53.81 tff(52,plain,
% 53.63/53.81 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1))))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(53,plain,
% 53.63/53.81 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1))))))),
% 53.63/53.81 inference(quant_inst,[status(thm)],[])).
% 53.63/53.81 tff(54,plain,
% 53.63/53.81 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1)))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[53, 52])).
% 53.63/53.81 tff(55,plain,
% 53.63/53.81 (~(v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1))))),
% 53.63/53.81 inference(unit_resolution,[status(thm)],[54, 32, 31, 30, 29, 51])).
% 53.63/53.81 tff(56,plain,
% 53.63/53.81 ((v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1)))) | v3_lattices(k11_group_4(B!1))),
% 53.63/53.81 inference(tautology,[status(thm)],[])).
% 53.63/53.81 tff(57,plain,
% 53.63/53.81 (v3_lattices(k11_group_4(B!1))),
% 53.63/53.81 inference(unit_resolution,[status(thm)],[56, 55])).
% 53.63/53.81 tff(58,plain,
% 53.63/53.81 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 53.63/53.81 inference(bind,[status(th)],[])).
% 53.63/53.81 tff(59,plain,
% 53.63/53.81 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(quant_intro,[status(thm)],[58])).
% 53.63/53.81 tff(60,plain,
% 53.63/53.81 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(61,plain,
% 53.63/53.81 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 53.63/53.81 inference(bind,[status(th)],[])).
% 53.63/53.81 tff(62,plain,
% 53.63/53.81 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(quant_intro,[status(thm)],[61])).
% 53.63/53.81 tff(63,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 53.63/53.81 tff(64,plain,
% 53.63/53.81 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[63, 62])).
% 53.63/53.81 tff(65,plain,
% 53.63/53.81 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[64, 60])).
% 53.63/53.81 tff(66,plain,(
% 53.63/53.81 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(skolemize,[status(sab)],[65])).
% 53.63/53.81 tff(67,plain,
% 53.63/53.81 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[66, 59])).
% 53.63/53.81 tff(68,plain,
% 53.63/53.81 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))) | (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))) | (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(69,plain,
% 53.63/53.81 (((k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1)))) <=> ((~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))) | (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(70,plain,
% 53.63/53.81 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))) | (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))),
% 53.63/53.81 inference(monotonicity,[status(thm)],[69])).
% 53.63/53.81 tff(71,plain,
% 53.63/53.81 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))) | (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.81 inference(transitivity,[status(thm)],[70, 68])).
% 53.63/53.81 tff(72,plain,
% 53.63/53.81 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))))),
% 53.63/53.81 inference(quant_inst,[status(thm)],[])).
% 53.63/53.81 tff(73,plain,
% 53.63/53.81 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(k11_group_4(B!1))) | (~l3_lattices(k11_group_4(B!1))) | (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[72, 71])).
% 53.63/53.81 tff(74,plain,
% 53.63/53.81 (k11_group_4(B!1) = g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))),
% 53.63/53.81 inference(unit_resolution,[status(thm)],[73, 67, 57, 38])).
% 53.63/53.81 tff(75,plain,
% 53.63/53.81 (g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))) = k11_group_4(B!1)),
% 53.63/53.81 inference(symmetry,[status(thm)],[74])).
% 53.63/53.81 tff(76,plain,
% 53.63/53.81 (u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) = u1_struct_0(k11_group_4(B!1))),
% 53.63/53.81 inference(monotonicity,[status(thm)],[75])).
% 53.63/53.81 tff(77,plain,
% 53.63/53.81 (v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) <=> v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))),
% 53.63/53.81 inference(monotonicity,[status(thm)],[76])).
% 53.63/53.81 tff(78,plain,
% 53.63/53.81 (v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))) <=> v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.81 inference(symmetry,[status(thm)],[77])).
% 53.63/53.81 tff(79,plain,
% 53.63/53.81 (^[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)))),
% 53.63/53.81 inference(bind,[status(th)],[])).
% 53.63/53.81 tff(80,plain,
% 53.63/53.81 (![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))),
% 53.63/53.81 inference(quant_intro,[status(thm)],[79])).
% 53.63/53.81 tff(81,plain,
% 53.63/53.81 (![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))),
% 53.63/53.81 inference(rewrite,[status(thm)],[])).
% 53.63/53.81 tff(82,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')).
% 53.63/53.81 tff(83,plain,
% 53.63/53.81 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[82, 81])).
% 53.63/53.81 tff(84,plain,(
% 53.63/53.81 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.63/53.81 inference(skolemize,[status(sab)],[83])).
% 53.63/53.81 tff(85,plain,
% 53.63/53.81 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.63/53.81 inference(modus_ponens,[status(thm)],[84, 80])).
% 53.63/53.81 tff(86,plain,
% 53.63/53.81 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 53.63/53.81 inference(quant_inst,[status(thm)],[])).
% 53.63/53.82 tff(87,plain,
% 53.63/53.82 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[86, 85])).
% 53.63/53.82 tff(88,plain,
% 53.63/53.82 (~(m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v2_funct_1(C!2)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 53.63/53.82 inference(and_elim,[status(thm)],[28])).
% 53.63/53.82 tff(89,plain,
% 53.63/53.82 (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(or_elim,[status(thm)],[88])).
% 53.63/53.82 tff(90,plain,
% 53.63/53.82 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(and_elim,[status(thm)],[89])).
% 53.63/53.82 tff(91,plain,
% 53.63/53.82 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(tautology,[status(thm)],[])).
% 53.63/53.82 tff(92,plain,
% 53.63/53.82 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[91, 90])).
% 53.63/53.82 tff(93,plain,
% 53.63/53.82 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[92, 87])).
% 53.63/53.82 tff(94,plain,
% 53.63/53.82 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))))),
% 53.63/53.82 inference(bind,[status(th)],[])).
% 53.63/53.82 tff(95,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))),
% 53.63/53.82 inference(quant_intro,[status(thm)],[94])).
% 53.63/53.82 tff(96,plain,
% 53.63/53.82 (^[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) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~(v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~(v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~(v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), rewrite((v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) <=> (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> ((v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))))), rewrite(((v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))))),
% 53.63/53.82 inference(bind,[status(th)],[])).
% 53.63/53.82 tff(97,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))),
% 53.63/53.82 inference(quant_intro,[status(thm)],[96])).
% 53.63/53.82 tff(98,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))),
% 53.63/53.82 inference(rewrite,[status(thm)],[])).
% 53.63/53.82 tff(99,plain,
% 53.63/53.82 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(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)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & v1_funct_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & v1_funct_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C)))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) <=> (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))),
% 53.63/53.82 inference(bind,[status(th)],[])).
% 53.63/53.82 tff(100,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))),
% 53.63/53.82 inference(quant_intro,[status(thm)],[99])).
% 53.63/53.82 tff(101,axiom,(![A: $i, B: $i, C: $i] : ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_latsubgr')).
% 53.63/53.82 tff(102,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[101, 100])).
% 53.63/53.82 tff(103,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[102, 98])).
% 53.63/53.82 tff(104,plain,(
% 53.63/53.82 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (v1_funct_1(k3_latsubgr(A, B, C)) & v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B))) & m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))),
% 53.63/53.82 inference(skolemize,[status(sab)],[103])).
% 53.63/53.82 tff(105,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[104, 97])).
% 53.63/53.82 tff(106,plain,
% 53.63/53.82 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[105, 95])).
% 53.63/53.82 tff(107,plain,
% 53.63/53.82 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 53.63/53.82 inference(and_elim,[status(thm)],[89])).
% 53.63/53.82 tff(108,plain,
% 53.63/53.82 (v1_funct_1(C!2)),
% 53.63/53.82 inference(and_elim,[status(thm)],[89])).
% 53.63/53.82 tff(109,plain,
% 53.63/53.82 (l1_group_1(A!0)),
% 53.63/53.82 inference(and_elim,[status(thm)],[28])).
% 53.63/53.82 tff(110,plain,
% 53.63/53.82 (v4_group_1(A!0)),
% 53.63/53.82 inference(and_elim,[status(thm)],[28])).
% 53.63/53.82 tff(111,plain,
% 53.63/53.82 (v3_group_1(A!0)),
% 53.63/53.82 inference(and_elim,[status(thm)],[28])).
% 53.63/53.82 tff(112,plain,
% 53.63/53.82 (~v3_struct_0(A!0)),
% 53.63/53.82 inference(and_elim,[status(thm)],[28])).
% 53.63/53.82 tff(113,plain,
% 53.63/53.82 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))),
% 53.63/53.82 inference(rewrite,[status(thm)],[])).
% 53.63/53.82 tff(114,plain,
% 53.63/53.82 ((v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))),
% 53.63/53.82 inference(rewrite,[status(thm)],[])).
% 53.63/53.82 tff(115,plain,
% 53.63/53.82 ((~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))) <=> (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))),
% 53.63/53.82 inference(rewrite,[status(thm)],[])).
% 53.63/53.82 tff(116,plain,
% 53.63/53.82 ((v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))),
% 53.63/53.82 inference(monotonicity,[status(thm)],[115])).
% 53.63/53.82 tff(117,plain,
% 53.63/53.82 ((v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))),
% 53.63/53.82 inference(transitivity,[status(thm)],[116, 114])).
% 53.63/53.82 tff(118,plain,
% 53.63/53.82 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))))),
% 53.63/53.82 inference(monotonicity,[status(thm)],[117])).
% 53.63/53.82 tff(119,plain,
% 53.63/53.82 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))),
% 53.63/53.82 inference(transitivity,[status(thm)],[118, 113])).
% 53.63/53.82 tff(120,plain,
% 53.63/53.82 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~v1_funct_1(C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))))),
% 53.63/53.82 inference(quant_inst,[status(thm)],[])).
% 53.63/53.82 tff(121,plain,
% 53.63/53.82 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~v1_funct_1(k3_latsubgr(A, B, C))) | (~v1_funct_2(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))) | (~m2_relset_1(k3_latsubgr(A, B, C), u1_struct_0(k11_group_4(A)), u1_struct_0(k11_group_4(B)))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[120, 119])).
% 53.63/53.82 tff(122,plain,
% 53.63/53.82 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[121, 112, 111, 110, 109, 32, 31, 30, 29, 108, 107, 106])).
% 53.63/53.82 tff(123,plain,
% 53.63/53.82 (~((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[122, 93])).
% 53.63/53.82 tff(124,plain,
% 53.63/53.82 (((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))) | v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))),
% 53.63/53.82 inference(tautology,[status(thm)],[])).
% 53.63/53.82 tff(125,plain,
% 53.63/53.82 (v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[124, 123])).
% 53.63/53.82 tff(126,plain,
% 53.63/53.82 (v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[125, 78])).
% 53.63/53.82 tff(127,plain,
% 53.63/53.82 (m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) <=> m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))),
% 53.63/53.82 inference(monotonicity,[status(thm)],[76])).
% 53.63/53.82 tff(128,plain,
% 53.63/53.82 (m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))) <=> m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.82 inference(symmetry,[status(thm)],[127])).
% 53.63/53.82 tff(129,plain,
% 53.63/53.82 (((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))) | m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))),
% 53.63/53.82 inference(tautology,[status(thm)],[])).
% 53.63/53.82 tff(130,plain,
% 53.63/53.82 (m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))),
% 53.63/53.82 inference(unit_resolution,[status(thm)],[129, 123])).
% 53.63/53.82 tff(131,plain,
% 53.63/53.82 (m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.82 inference(modus_ponens,[status(thm)],[130, 128])).
% 53.63/53.82 tff(132,plain,
% 53.63/53.82 (v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) <=> v3_struct_0(k11_group_4(B!1))),
% 53.63/53.82 inference(monotonicity,[status(thm)],[75])).
% 53.63/53.82 tff(133,plain,
% 53.63/53.82 (v3_struct_0(k11_group_4(B!1)) <=> v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.82 inference(symmetry,[status(thm)],[132])).
% 53.63/53.82 tff(134,plain,
% 53.63/53.82 ((~v3_struct_0(k11_group_4(B!1))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.63/53.82 inference(monotonicity,[status(thm)],[133])).
% 53.63/53.83 tff(135,plain,
% 53.63/53.83 ((v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1)))) | (~v3_struct_0(k11_group_4(B!1)))),
% 53.63/53.83 inference(tautology,[status(thm)],[])).
% 53.63/53.83 tff(136,plain,
% 53.63/53.83 (~v3_struct_0(k11_group_4(B!1))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[135, 55])).
% 53.63/53.83 tff(137,plain,
% 53.63/53.83 (~v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[136, 134])).
% 53.63/53.83 tff(138,plain,
% 53.63/53.83 (v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) <=> v10_lattices(k11_group_4(B!1))),
% 53.63/53.83 inference(monotonicity,[status(thm)],[75])).
% 53.63/53.83 tff(139,plain,
% 53.63/53.83 (v10_lattices(k11_group_4(B!1)) <=> v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.83 inference(symmetry,[status(thm)],[138])).
% 53.63/53.83 tff(140,plain,
% 53.63/53.83 ((v3_struct_0(k11_group_4(B!1)) | (~v3_lattices(k11_group_4(B!1))) | (~v10_lattices(k11_group_4(B!1))) | (~v4_lattices(k11_group_4(B!1))) | (~v5_lattices(k11_group_4(B!1))) | (~v6_lattices(k11_group_4(B!1))) | (~v7_lattices(k11_group_4(B!1))) | (~v8_lattices(k11_group_4(B!1))) | (~v9_lattices(k11_group_4(B!1))) | (~v13_lattices(k11_group_4(B!1))) | (~v14_lattices(k11_group_4(B!1))) | (~v15_lattices(k11_group_4(B!1)))) | v10_lattices(k11_group_4(B!1))),
% 53.63/53.83 inference(tautology,[status(thm)],[])).
% 53.63/53.83 tff(141,plain,
% 53.63/53.83 (v10_lattices(k11_group_4(B!1))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[140, 55])).
% 53.63/53.83 tff(142,plain,
% 53.63/53.83 (v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[141, 139])).
% 53.63/53.83 tff(143,plain,
% 53.63/53.83 (l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) <=> l3_lattices(k11_group_4(B!1))),
% 53.63/53.83 inference(monotonicity,[status(thm)],[75])).
% 53.63/53.83 tff(144,plain,
% 53.63/53.83 (l3_lattices(k11_group_4(B!1)) <=> l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.83 inference(symmetry,[status(thm)],[143])).
% 53.63/53.83 tff(145,plain,
% 53.63/53.83 (l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[38, 144])).
% 53.63/53.83 tff(146,plain,
% 53.63/53.83 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~l3_lattices(k11_group_4(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~l3_lattices(k11_group_4(A!0))))))),
% 53.63/53.83 inference(rewrite,[status(thm)],[])).
% 53.63/53.83 tff(147,plain,
% 53.63/53.83 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~l3_lattices(k11_group_4(A!0))))))),
% 53.63/53.83 inference(quant_inst,[status(thm)],[])).
% 53.63/53.83 tff(148,plain,
% 53.63/53.83 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~l3_lattices(k11_group_4(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~l3_lattices(k11_group_4(A!0)))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[147, 146])).
% 53.63/53.83 tff(149,plain,
% 53.63/53.83 (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~l3_lattices(k11_group_4(A!0))))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[148, 112, 111, 110, 109, 13])).
% 53.63/53.83 tff(150,plain,
% 53.63/53.83 ((v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~l3_lattices(k11_group_4(A!0)))) | l3_lattices(k11_group_4(A!0))),
% 53.63/53.83 inference(tautology,[status(thm)],[])).
% 53.63/53.83 tff(151,plain,
% 53.63/53.83 (l3_lattices(k11_group_4(A!0))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[150, 149])).
% 53.63/53.83 tff(152,plain,
% 53.63/53.83 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0))))))),
% 53.63/53.83 inference(rewrite,[status(thm)],[])).
% 53.63/53.83 tff(153,plain,
% 53.63/53.83 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0))))))),
% 53.63/53.83 inference(quant_inst,[status(thm)],[])).
% 53.63/53.83 tff(154,plain,
% 53.63/53.83 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~(v3_struct_0(k11_group_4(A)) | (~v3_lattices(k11_group_4(A))) | (~v10_lattices(k11_group_4(A))) | (~v4_lattices(k11_group_4(A))) | (~v5_lattices(k11_group_4(A))) | (~v6_lattices(k11_group_4(A))) | (~v7_lattices(k11_group_4(A))) | (~v8_lattices(k11_group_4(A))) | (~v9_lattices(k11_group_4(A))) | (~v13_lattices(k11_group_4(A))) | (~v14_lattices(k11_group_4(A))) | (~v15_lattices(k11_group_4(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0)))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[153, 152])).
% 53.63/53.83 tff(155,plain,
% 53.63/53.83 (~(v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0))))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[154, 112, 111, 110, 109, 51])).
% 53.63/53.83 tff(156,plain,
% 53.63/53.83 ((v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0)))) | v10_lattices(k11_group_4(A!0))),
% 53.63/53.83 inference(tautology,[status(thm)],[])).
% 53.63/53.83 tff(157,plain,
% 53.63/53.83 (v10_lattices(k11_group_4(A!0))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[156, 155])).
% 53.63/53.83 tff(158,plain,
% 53.63/53.83 ((v3_struct_0(k11_group_4(A!0)) | (~v3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | (~v4_lattices(k11_group_4(A!0))) | (~v5_lattices(k11_group_4(A!0))) | (~v6_lattices(k11_group_4(A!0))) | (~v7_lattices(k11_group_4(A!0))) | (~v8_lattices(k11_group_4(A!0))) | (~v9_lattices(k11_group_4(A!0))) | (~v13_lattices(k11_group_4(A!0))) | (~v14_lattices(k11_group_4(A!0))) | (~v15_lattices(k11_group_4(A!0)))) | (~v3_struct_0(k11_group_4(A!0)))),
% 53.63/53.83 inference(tautology,[status(thm)],[])).
% 53.63/53.83 tff(159,plain,
% 53.63/53.83 (~v3_struct_0(k11_group_4(A!0))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[158, 155])).
% 53.63/53.83 tff(160,plain,
% 53.63/53.83 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))))),
% 53.63/53.83 inference(bind,[status(th)],[])).
% 53.63/53.83 tff(161,plain,
% 53.63/53.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))),
% 53.63/53.83 inference(quant_intro,[status(thm)],[160])).
% 53.63/53.83 tff(162,plain,
% 53.63/53.83 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))))),
% 53.63/53.83 inference(bind,[status(th)],[])).
% 53.63/53.83 tff(163,plain,
% 53.63/53.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))),
% 53.63/53.83 inference(quant_intro,[status(thm)],[162])).
% 53.63/53.83 tff(164,plain,
% 53.63/53.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))),
% 53.63/53.83 inference(transitivity,[status(thm)],[163, 161])).
% 53.63/53.83 tff(165,plain,
% 53.63/53.83 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) <=> (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) <=> (~(~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))), rewrite((~(~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), trans(trans(monotonicity(rewrite((m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)) <=> (~((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))))), ((m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))) <=> (m1_lattice4(C, A, B) <=> (~((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))))))), rewrite((m1_lattice4(C, A, B) <=> (~((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))))) <=> (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))), ((m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))) <=> (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))), rewrite((~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))) <=> (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))), ((m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))) <=> (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> ((v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))), rewrite(((v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))))),
% 53.63/53.83 inference(bind,[status(th)],[])).
% 53.63/53.83 tff(166,plain,
% 53.63/53.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))),
% 53.63/53.83 inference(quant_intro,[status(thm)],[165])).
% 53.63/53.83 tff(167,plain,
% 53.63/53.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))),
% 53.63/53.83 inference(rewrite,[status(thm)],[])).
% 53.63/53.83 tff(168,plain,
% 53.63/53.83 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))))), (![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))))),
% 53.63/53.83 inference(bind,[status(th)],[])).
% 53.63/53.83 tff(169,plain,
% 53.63/53.83 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))),
% 53.63/53.83 inference(quant_intro,[status(thm)],[168])).
% 53.63/53.83 tff(170,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t11_vectsp_8')).
% 53.63/53.83 tff(171,plain,
% 53.63/53.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[170, 169])).
% 53.63/53.83 tff(172,plain,
% 53.63/53.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[171, 167])).
% 53.63/53.83 tff(173,plain,(
% 53.63/53.83 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (m1_lattice4(C, A, B) <=> (m4_vectsp_8(C, A, B) & m3_vectsp_8(C, A, B))))))),
% 53.63/53.83 inference(skolemize,[status(sab)],[172])).
% 53.63/53.83 tff(174,plain,
% 53.63/53.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[173, 166])).
% 53.63/53.83 tff(175,plain,
% 53.63/53.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[174, 164])).
% 53.63/53.83 tff(176,plain,
% 53.63/53.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))) | (v3_struct_0(k11_group_4(A!0)) | (~l3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))) | v3_struct_0(k11_group_4(A!0)) | (~l3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B))))))),
% 53.63/53.83 inference(rewrite,[status(thm)],[])).
% 53.63/53.83 tff(177,plain,
% 53.63/53.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))) | (v3_struct_0(k11_group_4(A!0)) | (~l3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B))))))),
% 53.63/53.83 inference(quant_inst,[status(thm)],[])).
% 53.63/53.83 tff(178,plain,
% 53.63/53.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, A, B)) | (~m4_vectsp_8(C, A, B))) <=> m1_lattice4(C, A, B))))))) | v3_struct_0(k11_group_4(A!0)) | (~l3_lattices(k11_group_4(A!0))) | (~v10_lattices(k11_group_4(A!0))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B)))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[177, 176])).
% 53.63/53.83 tff(179,plain,
% 53.63/53.83 (![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B)))))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[178, 175, 159, 157, 151])).
% 53.63/53.83 tff(180,plain,
% 53.63/53.83 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B)))))) | (v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B)))))) | v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))))),
% 53.63/53.83 inference(rewrite,[status(thm)],[])).
% 53.63/53.83 tff(181,plain,
% 53.63/53.83 ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B)))))) | (v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))))),
% 53.63/53.83 inference(quant_inst,[status(thm)],[])).
% 53.63/53.83 tff(182,plain,
% 53.63/53.83 ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(B))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), B)) | (~m4_vectsp_8(C, k11_group_4(A!0), B))) <=> m1_lattice4(C, k11_group_4(A!0), B)))))) | v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))),
% 53.63/53.83 inference(modus_ponens,[status(thm)],[181, 180])).
% 53.63/53.83 tff(183,plain,
% 53.63/53.83 (v3_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) | (~l3_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~v10_lattices(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[182, 179])).
% 53.63/53.83 tff(184,plain,
% 53.63/53.83 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[183, 145, 142, 137])).
% 53.63/53.83 tff(185,plain,
% 53.63/53.83 (((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1)))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(k11_group_4(B!1))))) | v1_funct_1(k3_latsubgr(A!0, B!1, C!2))),
% 53.63/53.83 inference(tautology,[status(thm)],[])).
% 53.63/53.83 tff(186,plain,
% 53.63/53.83 (v1_funct_1(k3_latsubgr(A!0, B!1, C!2))),
% 53.63/53.83 inference(unit_resolution,[status(thm)],[185, 123])).
% 53.63/53.83 tff(187,plain,
% 53.63/53.83 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))) | ((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))) | (~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))),
% 53.67/53.84 inference(rewrite,[status(thm)],[])).
% 53.67/53.84 tff(188,plain,
% 53.67/53.84 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))) | ((~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))),
% 53.67/53.84 inference(quant_inst,[status(thm)],[])).
% 53.67/53.84 tff(189,plain,
% 53.67/53.84 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(C, u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(C, k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))))) | (~v1_funct_1(k3_latsubgr(A!0, B!1, C!2))) | (~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[188, 187])).
% 53.67/53.84 tff(190,plain,
% 53.67/53.84 ((~v1_funct_2(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~m2_relset_1(k3_latsubgr(A!0, B!1, C!2), u1_struct_0(k11_group_4(A!0)), u1_struct_0(g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | (~(((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))),
% 53.67/53.84 inference(unit_resolution,[status(thm)],[189, 186, 184])).
% 53.67/53.84 tff(191,plain,
% 53.67/53.84 (~(((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.67/53.84 inference(unit_resolution,[status(thm)],[190, 131, 126])).
% 53.67/53.84 tff(192,plain,
% 53.67/53.84 (m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.67/53.84 inference(monotonicity,[status(thm)],[75])).
% 53.67/53.84 tff(193,plain,
% 53.67/53.84 (m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.67/53.84 inference(symmetry,[status(thm)],[192])).
% 53.67/53.84 tff(194,plain,
% 53.67/53.84 ((~m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))) <=> (~m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.67/53.84 inference(monotonicity,[status(thm)],[193])).
% 53.67/53.84 tff(195,plain,
% 53.67/53.84 (~m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.67/53.84 inference(or_elim,[status(thm)],[88])).
% 53.67/53.84 tff(196,plain,
% 53.67/53.84 (~m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[195, 194])).
% 53.67/53.84 tff(197,plain,
% 53.67/53.84 (m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) <=> m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.67/53.84 inference(monotonicity,[status(thm)],[75])).
% 53.67/53.84 tff(198,plain,
% 53.67/53.84 (m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) <=> m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.67/53.84 inference(symmetry,[status(thm)],[197])).
% 53.67/53.84 tff(199,plain,
% 53.67/53.84 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))),
% 53.67/53.84 inference(bind,[status(th)],[])).
% 53.67/53.84 tff(200,plain,
% 53.67/53.84 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.84 inference(quant_intro,[status(thm)],[199])).
% 53.67/53.84 tff(201,plain,
% 53.67/53.84 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))),
% 53.67/53.84 inference(bind,[status(th)],[])).
% 53.67/53.84 tff(202,plain,
% 53.67/53.84 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.84 inference(quant_intro,[status(thm)],[201])).
% 53.67/53.84 tff(203,plain,
% 53.67/53.84 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.84 inference(transitivity,[status(thm)],[202, 200])).
% 53.67/53.84 tff(204,plain,
% 53.67/53.84 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) <=> (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), ((m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), rewrite((m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))) <=> (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))), ((m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), (![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), (((~((~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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), (((~((~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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))))),
% 53.67/53.84 inference(bind,[status(th)],[])).
% 53.67/53.84 tff(205,plain,
% 53.67/53.84 (![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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.84 inference(quant_intro,[status(thm)],[204])).
% 53.67/53.84 tff(206,plain,
% 53.67/53.84 (![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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, 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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.67/53.84 inference(rewrite,[status(thm)],[])).
% 53.67/53.84 tff(207,plain,
% 53.67/53.84 (^[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(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite((v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> ((~v2_funct_1(C)) | m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((~v2_funct_1(C)) | m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((~v2_funct_1(C)) | m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))), (![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), ((((((~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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))) <=> (((~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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))), rewrite((((~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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ((~((~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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), ((((((~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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))) <=> ((~((~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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))))),
% 53.67/53.84 inference(bind,[status(th)],[])).
% 53.67/53.84 tff(208,plain,
% 53.67/53.84 (![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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.67/53.84 inference(quant_intro,[status(thm)],[207])).
% 53.67/53.84 tff(209,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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v2_funct_1(C) => m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t36_latsubgr')).
% 53.67/53.84 tff(210,plain,
% 53.67/53.84 (![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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[209, 208])).
% 53.67/53.84 tff(211,plain,
% 53.67/53.84 (![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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[210, 206])).
% 53.67/53.84 tff(212,plain,(
% 53.67/53.84 ![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] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 53.67/53.84 inference(skolemize,[status(sab)],[211])).
% 53.67/53.84 tff(213,plain,
% 53.67/53.84 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[212, 205])).
% 53.67/53.84 tff(214,plain,
% 53.67/53.84 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[213, 203])).
% 53.67/53.84 tff(215,plain,
% 53.67/53.84 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)))))),
% 53.67/53.84 inference(rewrite,[status(thm)],[])).
% 53.67/53.84 tff(216,plain,
% 53.67/53.84 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)))))),
% 53.67/53.84 inference(rewrite,[status(thm)],[])).
% 53.67/53.84 tff(217,plain,
% 53.67/53.84 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))))),
% 53.67/53.84 inference(monotonicity,[status(thm)],[216])).
% 53.67/53.84 tff(218,plain,
% 53.67/53.84 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)))))),
% 53.67/53.84 inference(transitivity,[status(thm)],[217, 215])).
% 53.67/53.84 tff(219,plain,
% 53.67/53.84 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))),
% 53.67/53.84 inference(quant_inst,[status(thm)],[])).
% 53.67/53.84 tff(220,plain,
% 53.67/53.84 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m3_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))),
% 53.67/53.84 inference(modus_ponens,[status(thm)],[219, 218])).
% 53.67/53.84 tff(221,plain,
% 53.67/53.84 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))),
% 53.67/53.84 inference(unit_resolution,[status(thm)],[220, 112, 111, 110, 109, 214])).
% 53.67/53.84 tff(222,plain,
% 53.67/53.84 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1))))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(223,plain,
% 53.67/53.85 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1))))),
% 53.67/53.85 inference(quant_inst,[status(thm)],[])).
% 53.67/53.85 tff(224,plain,
% 53.67/53.85 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)) | m3_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[223, 222])).
% 53.67/53.85 tff(225,plain,
% 53.67/53.85 (![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.85 inference(unit_resolution,[status(thm)],[224, 32, 31, 30, 29, 221])).
% 53.67/53.85 tff(226,plain,
% 53.67/53.85 (v1_group_6(C!2, A!0, B!1)),
% 53.67/53.85 inference(and_elim,[status(thm)],[89])).
% 53.67/53.85 tff(227,plain,
% 53.67/53.85 (v2_funct_1(C!2)),
% 53.67/53.85 inference(or_elim,[status(thm)],[88])).
% 53.67/53.85 tff(228,plain,
% 53.67/53.85 (((~![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)))) | ((~v2_funct_1(C!2)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))) <=> ((~![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)))) | (~v2_funct_1(C!2)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(229,plain,
% 53.67/53.85 ((~![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)))) | ((~v2_funct_1(C!2)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.85 inference(quant_inst,[status(thm)],[])).
% 53.67/53.85 tff(230,plain,
% 53.67/53.85 ((~![C: $i] : ((~v2_funct_1(C)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)))) | (~v2_funct_1(C!2)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[229, 228])).
% 53.67/53.85 tff(231,plain,
% 53.67/53.85 (m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.67/53.85 inference(unit_resolution,[status(thm)],[230, 227, 108, 107, 226, 90, 225])).
% 53.67/53.85 tff(232,plain,
% 53.67/53.85 (m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[231, 198])).
% 53.67/53.85 tff(233,plain,
% 53.67/53.85 (m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))) <=> m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.67/53.85 inference(monotonicity,[status(thm)],[75])).
% 53.67/53.85 tff(234,plain,
% 53.67/53.85 (m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) <=> m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.67/53.85 inference(symmetry,[status(thm)],[233])).
% 53.67/53.85 tff(235,plain,
% 53.67/53.85 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))),
% 53.67/53.85 inference(bind,[status(th)],[])).
% 53.67/53.85 tff(236,plain,
% 53.67/53.85 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.85 inference(quant_intro,[status(thm)],[235])).
% 53.67/53.85 tff(237,plain,
% 53.67/53.85 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))),
% 53.67/53.85 inference(bind,[status(th)],[])).
% 53.67/53.85 tff(238,plain,
% 53.67/53.85 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.85 inference(quant_intro,[status(thm)],[237])).
% 53.67/53.85 tff(239,plain,
% 53.67/53.85 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.85 inference(transitivity,[status(thm)],[238, 236])).
% 53.67/53.85 tff(240,plain,
% 53.67/53.85 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) <=> (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), (((~((~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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))), (((~((~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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))))),
% 53.67/53.85 inference(bind,[status(th)],[])).
% 53.67/53.85 tff(241,plain,
% 53.67/53.85 (![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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.85 inference(quant_intro,[status(thm)],[240])).
% 53.67/53.85 tff(242,plain,
% 53.67/53.85 (![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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(243,plain,
% 53.67/53.85 (^[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(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))))), (![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))), ((((((~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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> (((~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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))))), rewrite((((~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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> ((~((~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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))), ((((((~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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B))))) <=> ((~((~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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))))),
% 53.67/53.85 inference(bind,[status(th)],[])).
% 53.67/53.85 tff(244,plain,
% 53.67/53.85 (![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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))),
% 53.67/53.85 inference(quant_intro,[status(thm)],[243])).
% 53.67/53.85 tff(245,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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_latsubgr')).
% 53.67/53.85 tff(246,plain,
% 53.67/53.85 (![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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[245, 244])).
% 53.67/53.85 tff(247,plain,
% 53.67/53.85 (![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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[246, 242])).
% 53.67/53.85 tff(248,plain,(
% 53.67/53.85 ![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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)))))),
% 53.67/53.85 inference(skolemize,[status(sab)],[247])).
% 53.67/53.85 tff(249,plain,
% 53.67/53.85 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[248, 241])).
% 53.67/53.85 tff(250,plain,
% 53.67/53.85 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[249, 239])).
% 53.67/53.85 tff(251,plain,
% 53.67/53.85 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(252,plain,
% 53.67/53.85 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(253,plain,
% 53.67/53.85 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))))),
% 53.67/53.85 inference(monotonicity,[status(thm)],[252])).
% 53.67/53.85 tff(254,plain,
% 53.67/53.85 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))),
% 53.67/53.85 inference(transitivity,[status(thm)],[253, 251])).
% 53.67/53.85 tff(255,plain,
% 53.67/53.85 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B)))))),
% 53.67/53.85 inference(quant_inst,[status(thm)],[])).
% 53.67/53.85 tff(256,plain,
% 53.67/53.85 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (m4_vectsp_8(k3_latsubgr(A, B, C), k11_group_4(A), k11_group_4(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(C, A, B)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[255, 254])).
% 53.67/53.85 tff(257,plain,
% 53.67/53.85 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))),
% 53.67/53.85 inference(unit_resolution,[status(thm)],[256, 112, 111, 110, 109, 250])).
% 53.67/53.85 tff(258,plain,
% 53.67/53.85 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1))))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(259,plain,
% 53.67/53.85 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1)))) <=> (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1))))),
% 53.67/53.85 inference(rewrite,[status(thm)],[])).
% 53.67/53.85 tff(260,plain,
% 53.67/53.85 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))))),
% 53.67/53.85 inference(monotonicity,[status(thm)],[259])).
% 53.67/53.85 tff(261,plain,
% 53.67/53.85 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1))))),
% 53.67/53.85 inference(transitivity,[status(thm)],[260, 258])).
% 53.67/53.85 tff(262,plain,
% 53.67/53.85 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C, A!0, B!1))))),
% 53.67/53.85 inference(quant_inst,[status(thm)],[])).
% 53.67/53.85 tff(263,plain,
% 53.67/53.85 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | m4_vectsp_8(k3_latsubgr(A!0, B, C), k11_group_4(A!0), k11_group_4(B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(C, A!0, B))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))),
% 53.67/53.85 inference(modus_ponens,[status(thm)],[262, 261])).
% 53.67/53.85 tff(264,plain,
% 53.67/53.85 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))),
% 53.67/53.86 inference(unit_resolution,[status(thm)],[263, 32, 31, 30, 29, 257])).
% 53.67/53.86 tff(265,plain,
% 53.67/53.86 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.86 inference(rewrite,[status(thm)],[])).
% 53.67/53.86 tff(266,plain,
% 53.67/53.86 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C!2, A!0, B!1))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.86 inference(rewrite,[status(thm)],[])).
% 53.67/53.86 tff(267,plain,
% 53.67/53.86 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C!2, A!0, B!1)))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))))),
% 53.67/53.86 inference(monotonicity,[status(thm)],[266])).
% 53.67/53.86 tff(268,plain,
% 53.67/53.86 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C!2, A!0, B!1)))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)))),
% 53.67/53.86 inference(transitivity,[status(thm)],[267, 265])).
% 53.67/53.86 tff(269,plain,
% 53.67/53.86 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C!2, A!0, B!1)))),
% 53.93/54.11 inference(quant_inst,[status(thm)],[])).
% 53.93/54.11 tff(270,plain,
% 53.93/54.11 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C), k11_group_4(A!0), k11_group_4(B!1)) | (~v1_group_6(C, A!0, B!1)))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_group_6(C!2, A!0, B!1)) | m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.93/54.11 inference(modus_ponens,[status(thm)],[269, 268])).
% 53.93/54.11 tff(271,plain,
% 53.93/54.11 (m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), k11_group_4(B!1))),
% 53.93/54.11 inference(unit_resolution,[status(thm)],[270, 108, 107, 226, 90, 264])).
% 53.93/54.11 tff(272,plain,
% 53.93/54.11 (m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.93/54.11 inference(modus_ponens,[status(thm)],[271, 234])).
% 53.93/54.11 tff(273,plain,
% 53.93/54.11 ((~((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))) | (~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))),
% 53.93/54.11 inference(tautology,[status(thm)],[])).
% 53.93/54.11 tff(274,plain,
% 53.93/54.11 (~((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))))),
% 53.93/54.11 inference(unit_resolution,[status(thm)],[273, 272, 232])).
% 53.93/54.11 tff(275,plain,
% 53.93/54.11 ((((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) <=> m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | ((~m3_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))) | (~m4_vectsp_8(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1)))))) | m1_lattice4(k3_latsubgr(A!0, B!1, C!2), k11_group_4(A!0), g3_lattices(u1_struct_0(k11_group_4(B!1)), u2_lattices(k11_group_4(B!1)), u1_lattices(k11_group_4(B!1))))),
% 53.93/54.11 inference(tautology,[status(thm)],[])).
% 53.93/54.11 tff(276,plain,
% 53.93/54.11 ($false),
% 53.93/54.11 inference(unit_resolution,[status(thm)],[275, 274, 196, 191])).
% 53.93/54.11 % SZS output end Proof
% 53.97/54.14 % E exiting
%------------------------------------------------------------------------------