%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT331+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 05:14:23 AM UTC 2025
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT331+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 20:22:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(k8_filter_0_type, type, (
% 0.21/0.46 k8_filter_0: ( $i * $i ) > $i)).
% 0.21/0.46 tff(tptp_fun_C_2_type, type, (
% 0.21/0.46 tptp_fun_C_2: $i)).
% 0.21/0.46 tff(tptp_fun_B_1_type, type, (
% 0.21/0.46 tptp_fun_B_1: $i)).
% 0.21/0.46 tff(tptp_fun_A_0_type, type, (
% 0.21/0.46 tptp_fun_A_0: $i)).
% 0.21/0.46 tff(g3_lattices_type, type, (
% 0.21/0.46 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.21/0.46 tff(k1_realset1_type, type, (
% 0.21/0.46 k1_realset1: ( $i * $i ) > $i)).
% 0.21/0.46 tff(u1_lattices_type, type, (
% 0.21/0.46 u1_lattices: $i > $i)).
% 0.21/0.46 tff(u2_lattices_type, type, (
% 0.21/0.46 u2_lattices: $i > $i)).
% 0.21/0.46 tff(m2_relset_1_type, type, (
% 0.21/0.46 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.21/0.46 tff(k2_zfmisc_1_type, type, (
% 0.21/0.46 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.21/0.46 tff(v1_funct_2_type, type, (
% 0.21/0.46 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.21/0.46 tff(v1_funct_1_type, type, (
% 0.21/0.46 v1_funct_1: $i > $o)).
% 0.21/0.46 tff(v10_lattices_type, type, (
% 0.21/0.46 v10_lattices: $i > $o)).
% 0.21/0.46 tff(l3_lattices_type, type, (
% 0.21/0.46 l3_lattices: $i > $o)).
% 0.21/0.46 tff(v3_struct_0_type, type, (
% 0.21/0.46 v3_struct_0: $i > $o)).
% 0.21/0.46 tff(m1_filter_0_type, type, (
% 0.21/0.46 m1_filter_0: ( $i * $i ) > $o)).
% 0.21/0.46 tff(m1_filter_2_type, type, (
% 0.21/0.46 m1_filter_2: ( $i * $i ) > $o)).
% 0.21/0.46 tff(u1_struct_0_type, type, (
% 0.21/0.46 u1_struct_0: $i > $i)).
% 0.21/0.46 tff(m1_relset_1_type, type, (
% 0.21/0.46 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.21/0.46 tff(l2_lattices_type, type, (
% 0.21/0.46 l2_lattices: $i > $o)).
% 0.21/0.46 tff(l1_lattices_type, type, (
% 0.21/0.46 l1_lattices: $i > $o)).
% 0.21/0.46 tff(1,plain,
% 0.21/0.46 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(2,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(4,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(6,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[6, 4])).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 (^[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))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.46 tff(13,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 0.21/0.46 tff(14,plain,
% 0.21/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.46 tff(16,plain,(
% 0.21/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[15])).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 ((((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2))))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 ((~((~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))))) <=> (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 ((((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (~((~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))))) <=> (((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 ((((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (~((~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[23, 21])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (~((~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (~((~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[25, 20])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 ((~![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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 ((~![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] : (m1_filter_2(C, A) => ![D: $i] : (m1_filter_2(D, B) => (((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D)) => (k8_filter_0(A, C) = k8_filter_0(B, D)))))))) <=> (~![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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(29,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] : (m1_filter_2(C, A) => ![D: $i] : (m1_filter_2(D, B) => (((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D)) => (k8_filter_0(A, C) = k8_filter_0(B, D)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t68_filter_2')).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (~![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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (~![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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (~![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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (~![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] : ((~m1_filter_2(C, A)) | (~m1_filter_2(C, B)) | (k8_filter_0(A, C) = k8_filter_0(B, C)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (l3_lattices(B!1)),
% 0.21/0.47 inference(and_elim,[status(thm)],[34])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (v10_lattices(B!1)),
% 0.21/0.47 inference(and_elim,[status(thm)],[34])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (~v3_struct_0(B!1)),
% 0.21/0.47 inference(and_elim,[status(thm)],[34])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[40, 37, 36, 35, 19])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 ((~![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))) | (m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (~((~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~m1_filter_2(C!2, A!0)) | (~m1_filter_2(C!2, B!1)) | (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)))),
% 0.21/0.47 inference(and_elim,[status(thm)],[34])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (m1_filter_2(C!2, B!1)),
% 0.21/0.47 inference(or_elim,[status(thm)],[44])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 ((~(m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))) | (~m1_filter_2(C!2, B!1)) | m1_filter_0(C!2, B!1)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 ((~(m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))) | m1_filter_0(C!2, B!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (m1_filter_0(C!2, B!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[47, 43])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[52, 50])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (^[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] : rewrite(((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (^[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(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) <=> ((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))), rewrite(((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))) <=> ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))), (((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> (((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))), rewrite((((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))) <=> ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))), (((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), (![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))), ((m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> (m1_filter_0(B, A) => ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), rewrite((m1_filter_0(B, A) => ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))), ((m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))))), (![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(58,plain,
% 0.21/0.48 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.48 tff(59,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_filter_0')).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.48 tff(62,plain,(
% 0.21/0.48 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> (v1_funct_1(k1_realset1(u2_lattices(A), B)) & v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B))) & v1_funct_1(k1_realset1(u1_lattices(A), B)) & v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[61])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[67, 37, 36, 35, 64])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B))))))) | ((~m1_filter_0(C!2, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B))))))) | (~m1_filter_0(C!2, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 ((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B))))))) | ((~m1_filter_0(C!2, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 ((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(B!1), B), k1_realset1(u1_lattices(B!1), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), B))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(B!1, B))))))) | (~m1_filter_0(C!2, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 ((~m1_filter_0(C!2, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 (![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[72, 48])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)) <=> (~(v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) <=> (~(~(v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), rewrite(((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))) <=> (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ((v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))))), rewrite(((v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)))), rewrite((((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B))) <=> ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)) => ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)) => ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.48 tff(81,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_filter_0')).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.21/0.48 tff(84,plain,(
% 0.21/0.48 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[83])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 ((v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))) <=> (v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 ((~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))) <=> (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 ((v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))) <=> (v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 ((v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))) <=> (v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[90, 88])).
% 0.21/0.49 tff(92,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.49 tff(93,plain,
% 0.21/0.49 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[92, 87])).
% 0.21/0.49 tff(94,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~m1_filter_0(C!2, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(95,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.49 tff(96,plain,
% 0.21/0.49 ((~m1_filter_0(C!2, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[95, 37, 36, 35, 86])).
% 0.21/0.49 tff(97,plain,
% 0.21/0.49 (~(v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[96, 48])).
% 0.21/0.49 tff(98,plain,
% 0.21/0.49 ((v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))) | l3_lattices(k8_filter_0(B!1, C!2))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(99,plain,
% 0.21/0.49 (l3_lattices(k8_filter_0(B!1, C!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.49 tff(100,plain,
% 0.21/0.49 ((v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))) | v10_lattices(k8_filter_0(B!1, C!2))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(101,plain,
% 0.21/0.49 (v10_lattices(k8_filter_0(B!1, C!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.21/0.49 tff(102,plain,
% 0.21/0.49 ((v3_struct_0(k8_filter_0(B!1, C!2)) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~l3_lattices(k8_filter_0(B!1, C!2)))) | (~v3_struct_0(k8_filter_0(B!1, C!2)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 (~v3_struct_0(k8_filter_0(B!1, C!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[102, 97])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | (v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(105,plain,
% 0.21/0.49 ((v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(B!1, C!2) = k8_filter_0(B!1, C!2))))) <=> (v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(106,plain,
% 0.21/0.49 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | (v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(B!1, C!2) = k8_filter_0(B!1, C!2)))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | (v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.49 tff(107,plain,
% 0.21/0.49 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | (v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(B!1, C!2) = k8_filter_0(B!1, C!2)))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[106, 104])).
% 0.21/0.49 tff(108,plain,
% 0.21/0.49 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | (v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(B!1, C!2) = k8_filter_0(B!1, C!2)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(109,plain,
% 0.21/0.49 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(B!1, C!2)))))) | v3_struct_0(k8_filter_0(B!1, C!2)) | (~l3_lattices(k8_filter_0(B!1, C!2))) | (~v10_lattices(k8_filter_0(B!1, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (~((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[109, 103, 101, 99, 73])).
% 0.21/0.49 tff(111,plain,
% 0.21/0.49 (((~v1_funct_1(k1_realset1(u2_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(B!1), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(B!1), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2))))) | (k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 (k8_filter_0(B!1, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 (g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)) = k8_filter_0(B!1, C!2)),
% 0.21/0.50 inference(symmetry,[status(thm)],[112])).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))),
% 0.21/0.50 inference(or_elim,[status(thm)],[44])).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 (g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 0.21/0.50 inference(symmetry,[status(thm)],[114])).
% 0.21/0.50 tff(116,plain,
% 0.21/0.50 (^[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)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.50 tff(118,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(119,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')).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.50 tff(121,plain,(
% 0.21/0.50 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.50 inference(skolemize,[status(sab)],[120])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(128,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(131,plain,
% 0.21/0.50 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.50 tff(132,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.21/0.50 tff(133,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.50 tff(134,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.50 tff(135,plain,(
% 0.21/0.50 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[134])).
% 0.21/0.50 tff(136,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.21/0.50 tff(137,plain,
% 0.21/0.50 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.21/0.50 tff(138,plain,
% 0.21/0.50 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(139,plain,
% 0.21/0.50 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(140,plain,
% 0.21/0.50 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.50 tff(141,plain,
% 0.21/0.50 (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[140, 35, 137])).
% 0.21/0.50 tff(142,plain,
% 0.21/0.50 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l2_lattices(B!1)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(143,plain,
% 0.21/0.50 (l2_lattices(B!1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.21/0.50 tff(144,plain,
% 0.21/0.50 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(145,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.50 tff(146,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(147,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.50 tff(148,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(149,plain,
% 0.21/0.50 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(150,plain,
% 0.21/0.50 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.50 tff(151,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.21/0.50 tff(152,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.50 tff(153,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.21/0.50 tff(154,plain,(
% 0.21/0.50 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[153])).
% 0.21/0.50 tff(155,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.21/0.50 tff(156,plain,
% 0.21/0.50 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.21/0.50 tff(157,plain,
% 0.21/0.50 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(158,plain,
% 0.21/0.50 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(159,plain,
% 0.21/0.50 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.50 tff(160,plain,
% 0.21/0.50 ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[159, 156])).
% 0.21/0.50 tff(161,plain,
% 0.21/0.50 (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[160, 143])).
% 0.21/0.50 tff(162,plain,
% 0.21/0.50 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(163,plain,
% 0.21/0.50 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.21/0.50 tff(164,plain,
% 0.21/0.50 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(165,plain,
% 0.21/0.50 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.21/0.50 tff(166,plain,
% 0.21/0.50 (m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[165, 124])).
% 0.21/0.50 tff(167,plain,
% 0.21/0.50 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l1_lattices(B!1)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(168,plain,
% 0.21/0.50 (l1_lattices(B!1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[167, 141])).
% 0.21/0.50 tff(169,plain,
% 0.21/0.50 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(170,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[169])).
% 0.21/0.50 tff(171,plain,
% 0.21/0.50 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(172,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[171])).
% 0.21/0.50 tff(173,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(174,plain,
% 0.21/0.50 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(175,plain,
% 0.21/0.50 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[174])).
% 0.21/0.50 tff(176,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.21/0.50 tff(177,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.50 tff(178,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.21/0.50 tff(179,plain,(
% 0.21/0.50 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[178])).
% 0.21/0.50 tff(180,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.21/0.50 tff(181,plain,
% 0.21/0.50 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.21/0.50 tff(182,plain,
% 0.21/0.50 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(183,plain,
% 0.21/0.50 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(184,plain,
% 0.21/0.50 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.50 tff(185,plain,
% 0.21/0.50 ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[184, 181])).
% 0.21/0.50 tff(186,plain,
% 0.21/0.50 (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[185, 168])).
% 0.21/0.50 tff(187,plain,
% 0.21/0.50 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(188,plain,
% 0.21/0.50 (v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.21/0.50 tff(189,plain,
% 0.21/0.50 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u1_lattices(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(190,plain,
% 0.21/0.50 (v1_funct_1(u1_lattices(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[189, 186])).
% 0.21/0.50 tff(191,plain,
% 0.21/0.50 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(192,plain,
% 0.21/0.50 (v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[191, 161])).
% 0.21/0.50 tff(193,plain,
% 0.21/0.50 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u2_lattices(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(194,plain,
% 0.21/0.50 (v1_funct_1(u2_lattices(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[193, 161])).
% 0.21/0.50 tff(195,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(196,plain,
% 0.21/0.50 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[195, 122])).
% 0.21/0.50 tff(197,plain,
% 0.21/0.50 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[197, 186])).
% 0.21/0.50 tff(199,plain,
% 0.21/0.50 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(200,plain,
% 0.21/0.50 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.21/0.50 tff(201,plain,
% 0.21/0.50 (m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[200, 196])).
% 0.21/0.50 tff(202,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(203,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[202])).
% 0.21/0.50 tff(204,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(205,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.50 tff(206,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[205, 203])).
% 0.21/0.50 tff(207,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[207])).
% 0.21/0.50 tff(209,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(211,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[210])).
% 0.21/0.51 tff(212,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.21/0.51 tff(213,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.51 tff(214,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.21/0.51 tff(215,plain,(
% 0.21/0.51 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[214])).
% 0.21/0.51 tff(216,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.21/0.51 tff(217,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.21/0.51 tff(218,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(219,plain,
% 0.21/0.51 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) <=> ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(220,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[219])).
% 0.21/0.51 tff(221,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[220, 218])).
% 0.21/0.51 tff(222,plain,
% 0.21/0.51 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(223,plain,
% 0.21/0.51 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.51 tff(224,plain,
% 0.21/0.51 ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[223, 217])).
% 0.21/0.51 tff(225,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[224, 201, 194, 192, 190, 188, 166])).
% 0.21/0.51 tff(226,plain,
% 0.21/0.51 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(227,plain,
% 0.21/0.51 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(228,plain,
% 0.21/0.51 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[228, 225, 115])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_lattices(B!1) = u1_lattices(A!0))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 (u1_lattices(B!1) = u1_lattices(A!0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 (k1_realset1(u1_lattices(B!1), C!2) = k1_realset1(u1_lattices(A!0), C!2)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[231])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u2_lattices(B!1) = u2_lattices(A!0))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 (u2_lattices(B!1) = u2_lattices(A!0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[233, 229])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 (k1_realset1(u2_lattices(B!1), C!2) = k1_realset1(u2_lattices(A!0), C!2)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[234])).
% 0.21/0.51 tff(236,plain,
% 0.21/0.51 (g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2)) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[235, 232])).
% 0.21/0.51 tff(237,plain,
% 0.21/0.51 (g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)) = g3_lattices(C!2, k1_realset1(u2_lattices(B!1), C!2), k1_realset1(u1_lattices(B!1), C!2))),
% 0.21/0.51 inference(symmetry,[status(thm)],[236])).
% 0.21/0.51 tff(238,plain,
% 0.21/0.51 (l3_lattices(A!0)),
% 0.21/0.51 inference(and_elim,[status(thm)],[34])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 (v10_lattices(A!0)),
% 0.21/0.51 inference(and_elim,[status(thm)],[34])).
% 0.21/0.51 tff(240,plain,
% 0.21/0.51 (~v3_struct_0(A!0)),
% 0.21/0.51 inference(and_elim,[status(thm)],[34])).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 (![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[243, 240, 239, 238, 19])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 ((~![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))) | (m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(246,plain,
% 0.21/0.51 (m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 (m1_filter_2(C!2, A!0)),
% 0.21/0.51 inference(or_elim,[status(thm)],[44])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 ((~(m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))) | (~m1_filter_2(C!2, A!0)) | m1_filter_0(C!2, A!0)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(249,plain,
% 0.21/0.51 ((~(m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))) | m1_filter_0(C!2, A!0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.21/0.51 tff(250,plain,
% 0.21/0.51 (m1_filter_0(C!2, A!0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[249, 246])).
% 0.21/0.51 tff(251,plain,
% 0.21/0.51 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B)))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(252,plain,
% 0.21/0.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(253,plain,
% 0.21/0.52 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.21/0.52 tff(254,plain,
% 0.21/0.52 (![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[253, 240, 239, 238, 64])).
% 0.21/0.52 tff(255,plain,
% 0.21/0.52 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B))))))) | ((~m1_filter_0(C!2, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B))))))) | (~m1_filter_0(C!2, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(256,plain,
% 0.21/0.52 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B))))))) | ((~m1_filter_0(C!2, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(257,plain,
% 0.21/0.52 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k8_filter_0(A!0, B))))))) | (~m1_filter_0(C!2, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.21/0.52 tff(258,plain,
% 0.21/0.52 ((~m1_filter_0(C!2, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[257, 254])).
% 0.21/0.52 tff(259,plain,
% 0.21/0.52 (![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[258, 250])).
% 0.21/0.52 tff(260,plain,
% 0.21/0.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(261,plain,
% 0.21/0.52 ((v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(262,plain,
% 0.21/0.52 ((~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))) <=> (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(263,plain,
% 0.21/0.52 ((v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))) <=> (v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[262])).
% 0.21/0.52 tff(264,plain,
% 0.21/0.52 ((v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[263, 261])).
% 0.21/0.52 tff(265,plain,
% 0.21/0.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[264])).
% 0.21/0.52 tff(266,plain,
% 0.21/0.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[265, 260])).
% 0.21/0.52 tff(267,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~m1_filter_0(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(268,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.52 tff(269,plain,
% 0.21/0.52 ((~m1_filter_0(C!2, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[268, 240, 239, 238, 86])).
% 0.21/0.52 tff(270,plain,
% 0.21/0.52 (~(v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[269, 250])).
% 0.21/0.52 tff(271,plain,
% 0.21/0.52 ((v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))) | l3_lattices(k8_filter_0(A!0, C!2))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(272,plain,
% 0.21/0.52 (l3_lattices(k8_filter_0(A!0, C!2))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.21/0.52 tff(273,plain,
% 0.21/0.52 ((v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))) | v10_lattices(k8_filter_0(A!0, C!2))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(274,plain,
% 0.21/0.52 (v10_lattices(k8_filter_0(A!0, C!2))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[273, 270])).
% 0.21/0.52 tff(275,plain,
% 0.21/0.52 ((v3_struct_0(k8_filter_0(A!0, C!2)) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~l3_lattices(k8_filter_0(A!0, C!2)))) | (~v3_struct_0(k8_filter_0(A!0, C!2)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(276,plain,
% 0.21/0.52 (~v3_struct_0(k8_filter_0(A!0, C!2))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[275, 270])).
% 0.21/0.52 tff(277,plain,
% 0.21/0.52 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(278,plain,
% 0.21/0.52 ((v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(A!0, C!2) = k8_filter_0(A!0, C!2))))) <=> (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(279,plain,
% 0.21/0.52 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(A!0, C!2) = k8_filter_0(A!0, C!2)))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2))))))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[278])).
% 0.21/0.53 tff(280,plain,
% 0.21/0.53 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(A!0, C!2) = k8_filter_0(A!0, C!2)))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[279, 277])).
% 0.21/0.53 tff(281,plain,
% 0.21/0.53 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (k8_filter_0(A!0, C!2) = k8_filter_0(A!0, C!2)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(282,plain,
% 0.21/0.53 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(C = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2))) <=> (C = k8_filter_0(A!0, C!2)))))) | v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.53 tff(283,plain,
% 0.21/0.53 (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[282, 276, 274, 272, 259])).
% 0.21/0.53 tff(284,plain,
% 0.21/0.53 (((~v1_funct_1(k1_realset1(u2_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), C!2))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), C!2), k2_zfmisc_1(C!2, C!2), C!2)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2))))) | (k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(285,plain,
% 0.21/0.53 (k8_filter_0(A!0, C!2) = g3_lattices(C!2, k1_realset1(u2_lattices(A!0), C!2), k1_realset1(u1_lattices(A!0), C!2))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.21/0.53 tff(286,plain,
% 0.21/0.53 (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2)),
% 0.21/0.53 inference(transitivity,[status(thm)],[285, 237, 113])).
% 0.21/0.53 tff(287,plain,
% 0.21/0.53 (~(k8_filter_0(A!0, C!2) = k8_filter_0(B!1, C!2))),
% 0.21/0.53 inference(or_elim,[status(thm)],[44])).
% 0.21/0.53 tff(288,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[287, 286])).
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------