%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT347+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:27 AM UTC 2025
% Result : Theorem 0.92s 1.11s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT347+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 20:31:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.92/1.11 % SZS status Theorem
% 0.92/1.11 % SZS output start Proof
% 0.92/1.11 tff(m1_subset_1_type, type, (
% 0.92/1.11 m1_subset_1: ( $i * $i ) > $o)).
% 0.92/1.11 tff(k1_zfmisc_1_type, type, (
% 0.92/1.11 k1_zfmisc_1: $i > $i)).
% 0.92/1.11 tff(u1_struct_0_type, type, (
% 0.92/1.11 u1_struct_0: $i > $i)).
% 0.92/1.11 tff(k2_yellow_1_type, type, (
% 0.92/1.11 k2_yellow_1: $i > $i)).
% 0.92/1.11 tff(k8_waybel_0_type, type, (
% 0.92/1.11 k8_waybel_0: $i > $i)).
% 0.92/1.11 tff(g1_orders_2_type, type, (
% 0.92/1.11 g1_orders_2: ( $i * $i ) > $i)).
% 0.92/1.11 tff(k6_relset_1_type, type, (
% 0.92/1.11 k6_relset_1: ( $i * $i * $i ) > $i)).
% 0.92/1.11 tff(u1_orders_2_type, type, (
% 0.92/1.11 u1_orders_2: $i > $i)).
% 0.92/1.11 tff(tptp_fun_A_0_type, type, (
% 0.92/1.11 tptp_fun_A_0: $i)).
% 0.92/1.11 tff(tptp_fun_B_1_type, type, (
% 0.92/1.11 tptp_fun_B_1: $i)).
% 0.92/1.11 tff(k9_waybel_0_type, type, (
% 0.92/1.11 k9_waybel_0: $i > $i)).
% 0.92/1.11 tff(k7_lattice3_type, type, (
% 0.92/1.11 k7_lattice3: $i > $i)).
% 0.92/1.11 tff(v3_struct_0_type, type, (
% 0.92/1.11 v3_struct_0: $i > $o)).
% 0.92/1.11 tff(v2_lattice3_type, type, (
% 0.92/1.11 v2_lattice3: $i > $o)).
% 0.92/1.11 tff(l1_orders_2_type, type, (
% 0.92/1.11 l1_orders_2: $i > $o)).
% 0.92/1.11 tff(k3_tarski_type, type, (
% 0.92/1.11 k3_tarski: $i > $i)).
% 0.92/1.11 tff(k1_yellow_0_type, type, (
% 0.92/1.11 k1_yellow_0: ( $i * $i ) > $i)).
% 0.92/1.11 tff(v1_waybel_0_type, type, (
% 0.92/1.11 v1_waybel_0: ( $i * $i ) > $o)).
% 0.92/1.11 tff(v1_xboole_0_type, type, (
% 0.92/1.11 v1_xboole_0: $i > $o)).
% 0.92/1.11 tff(v2_yellow_0_type, type, (
% 0.92/1.11 v2_yellow_0: $i > $o)).
% 0.92/1.11 tff(v4_orders_2_type, type, (
% 0.92/1.11 v4_orders_2: $i > $o)).
% 0.92/1.11 tff(v3_orders_2_type, type, (
% 0.92/1.11 v3_orders_2: $i > $o)).
% 0.92/1.11 tff(v2_orders_2_type, type, (
% 0.92/1.11 v2_orders_2: $i > $o)).
% 0.92/1.11 tff(v1_yellow_0_type, type, (
% 0.92/1.11 v1_yellow_0: $i > $o)).
% 0.92/1.11 tff(v1_orders_2_type, type, (
% 0.92/1.11 v1_orders_2: $i > $o)).
% 0.92/1.11 tff(v1_lattice3_type, type, (
% 0.92/1.11 v1_lattice3: $i > $o)).
% 0.92/1.11 tff(1,plain,
% 0.92/1.11 (^[A: $i] : refl(((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(2,plain,
% 0.92/1.11 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[1])).
% 0.92/1.11 tff(3,plain,
% 0.92/1.11 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(4,plain,
% 0.92/1.11 (^[A: $i] : trans(monotonicity(rewrite((v2_lattice3(A) => (~v3_struct_0(A))) <=> ((~v2_lattice3(A)) | (~v3_struct_0(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> (l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))))), rewrite((l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(5,plain,
% 0.92/1.11 (![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[4])).
% 0.92/1.11 tff(6,axiom,(![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_lattice3')).
% 0.92/1.11 tff(7,plain,
% 0.92/1.11 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.92/1.11 tff(8,plain,
% 0.92/1.11 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.92/1.11 tff(9,plain,(
% 0.92/1.11 ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[8])).
% 0.92/1.11 tff(10,plain,
% 0.92/1.11 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.92/1.11 tff(11,plain,
% 0.92/1.11 (((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0)) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))))) <=> (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(12,plain,
% 0.92/1.11 ((~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B)))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(13,plain,
% 0.92/1.11 ((~![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v2_yellow_0(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B)))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(14,axiom,(~![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v2_yellow_0(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_waybel22')).
% 0.92/1.11 tff(15,plain,
% 0.92/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.92/1.11 tff(16,plain,
% 0.92/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.92/1.11 tff(17,plain,
% 0.92/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.92/1.11 tff(18,plain,
% 0.92/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.92/1.11 tff(19,plain,
% 0.92/1.11 (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.92/1.11 tff(20,plain,
% 0.92/1.11 (l1_orders_2(A!0)),
% 0.92/1.11 inference(and_elim,[status(thm)],[19])).
% 0.92/1.11 tff(21,plain,
% 0.92/1.11 (v2_lattice3(A!0)),
% 0.92/1.11 inference(and_elim,[status(thm)],[19])).
% 0.92/1.11 tff(22,plain,
% 0.92/1.11 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(23,plain,
% 0.92/1.11 (((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0))) <=> ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(24,plain,
% 0.92/1.11 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[23])).
% 0.92/1.11 tff(25,plain,
% 0.92/1.11 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[24, 22])).
% 0.92/1.11 tff(26,plain,
% 0.92/1.11 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(27,plain,
% 0.92/1.11 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.92/1.11 tff(28,plain,
% 0.92/1.11 (~v3_struct_0(A!0)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[27, 21, 20, 10])).
% 0.92/1.11 tff(29,plain,
% 0.92/1.11 (^[A: $i] : refl((v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) <=> (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(30,plain,
% 0.92/1.11 (![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) <=> ![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[29])).
% 0.92/1.11 tff(31,plain,
% 0.92/1.11 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(32,plain,
% 0.92/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[31])).
% 0.92/1.11 tff(33,plain,
% 0.92/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(34,plain,
% 0.92/1.11 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A)) & l1_orders_2(A)))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)))), ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))), ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(35,plain,
% 0.92/1.11 (![A: $i] : (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[34])).
% 0.92/1.11 tff(36,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_waybel16')).
% 0.92/1.11 tff(37,plain,
% 0.92/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.92/1.11 tff(38,plain,
% 0.92/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.92/1.11 tff(39,plain,(
% 0.92/1.11 ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 0.92/1.11 inference(skolemize,[status(sab)],[38])).
% 0.92/1.11 tff(40,plain,
% 0.92/1.11 (![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.92/1.11 tff(41,plain,
% 0.92/1.11 (![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.92/1.11 tff(42,plain,
% 0.92/1.11 (v3_orders_2(A!0)),
% 0.92/1.11 inference(and_elim,[status(thm)],[19])).
% 0.92/1.11 tff(43,plain,
% 0.92/1.11 (v2_orders_2(A!0)),
% 0.92/1.11 inference(and_elim,[status(thm)],[19])).
% 0.92/1.11 tff(44,plain,
% 0.92/1.11 (((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | ((~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(45,plain,
% 0.92/1.11 ((v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0))) <=> ((~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(46,plain,
% 0.92/1.11 (((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | ((~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0)))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[45])).
% 0.92/1.11 tff(47,plain,
% 0.92/1.11 (((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))),
% 0.92/1.11 inference(transitivity,[status(thm)],[46, 44])).
% 0.92/1.11 tff(48,plain,
% 0.92/1.11 ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(49,plain,
% 0.92/1.11 ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.92/1.11 tff(50,plain,
% 0.92/1.11 (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0)))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[49, 43, 42, 20, 41])).
% 0.92/1.11 tff(51,plain,
% 0.92/1.11 (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[50, 28])).
% 0.92/1.11 tff(52,plain,
% 0.92/1.11 (k8_waybel_0(k7_lattice3(A!0)) = k9_waybel_0(A!0)),
% 0.92/1.11 inference(symmetry,[status(thm)],[51])).
% 0.92/1.11 tff(53,plain,
% 0.92/1.11 (^[A: $i] : refl(((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(54,plain,
% 0.92/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[53])).
% 0.92/1.11 tff(55,plain,
% 0.92/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(56,plain,
% 0.92/1.11 (^[A: $i] : rewrite((l1_orders_2(A) => (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(57,plain,
% 0.92/1.11 (![A: $i] : (l1_orders_2(A) => (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[56])).
% 0.92/1.11 tff(58,axiom,(![A: $i] : (l1_orders_2(A) => (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_lattice3')).
% 0.92/1.11 tff(59,plain,
% 0.92/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.92/1.11 tff(60,plain,
% 0.92/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.92/1.11 tff(61,plain,(
% 0.92/1.11 ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(skolemize,[status(sab)],[60])).
% 0.92/1.11 tff(62,plain,
% 0.92/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.92/1.11 tff(63,plain,
% 0.92/1.11 (((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | ((~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | (~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(64,plain,
% 0.92/1.11 ((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | ((~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(65,plain,
% 0.92/1.11 ((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | (~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.92/1.11 tff(66,plain,
% 0.92/1.11 (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[65, 20, 62])).
% 0.92/1.11 tff(67,plain,
% 0.92/1.11 (g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))) = k7_lattice3(A!0)),
% 0.92/1.11 inference(symmetry,[status(thm)],[66])).
% 0.92/1.11 tff(68,plain,
% 0.92/1.11 (k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) = k8_waybel_0(k7_lattice3(A!0))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[67])).
% 0.92/1.12 tff(69,plain,
% 0.92/1.12 (k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) = k9_waybel_0(A!0)),
% 0.92/1.12 inference(transitivity,[status(thm)],[68, 52])).
% 0.92/1.12 tff(70,plain,
% 0.92/1.12 (k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) = k2_yellow_1(k9_waybel_0(A!0))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[69])).
% 0.92/1.12 tff(71,plain,
% 0.92/1.12 (u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))) = u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[70])).
% 0.92/1.12 tff(72,plain,
% 0.92/1.12 (k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) = k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[71])).
% 0.92/1.12 tff(73,plain,
% 0.92/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))) <=> m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[72])).
% 0.92/1.12 tff(74,plain,
% 0.92/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))) <=> m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))),
% 0.92/1.12 inference(symmetry,[status(thm)],[73])).
% 0.92/1.12 tff(75,plain,
% 0.92/1.12 (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)))),
% 0.92/1.12 inference(and_elim,[status(thm)],[19])).
% 0.92/1.12 tff(76,plain,
% 0.92/1.12 ((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))))),
% 0.92/1.12 inference(or_elim,[status(thm)],[75])).
% 0.92/1.12 tff(77,plain,
% 0.92/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))))),
% 0.92/1.12 inference(and_elim,[status(thm)],[76])).
% 0.92/1.12 tff(78,plain,
% 0.92/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.92/1.12 tff(79,plain,
% 0.92/1.12 (v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))) <=> v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[70])).
% 0.92/1.12 tff(80,plain,
% 0.92/1.12 (v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) <=> v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))),
% 0.92/1.12 inference(symmetry,[status(thm)],[79])).
% 0.92/1.12 tff(81,plain,
% 0.92/1.12 (v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0)))),
% 0.92/1.12 inference(and_elim,[status(thm)],[76])).
% 0.92/1.12 tff(82,plain,
% 0.92/1.12 (v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.92/1.12 tff(83,plain,
% 0.92/1.12 (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1)),
% 0.92/1.12 inference(monotonicity,[status(thm)],[70])).
% 0.92/1.12 tff(84,plain,
% 0.92/1.12 ((k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) <=> (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[83])).
% 0.92/1.12 tff(85,plain,
% 0.92/1.12 ((k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)) <=> (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1))),
% 0.96/1.12 inference(symmetry,[status(thm)],[84])).
% 0.96/1.12 tff(86,plain,
% 0.96/1.12 ((~(k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))) <=> (~(k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[85])).
% 0.96/1.12 tff(87,plain,
% 0.96/1.12 (~(k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))),
% 0.96/1.12 inference(or_elim,[status(thm)],[75])).
% 0.96/1.12 tff(88,plain,
% 0.96/1.12 (~(k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.96/1.12 tff(89,plain,
% 0.96/1.12 (v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v1_yellow_0(k7_lattice3(A!0))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[67])).
% 0.96/1.12 tff(90,plain,
% 0.96/1.12 (v1_yellow_0(k7_lattice3(A!0)) <=> v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(symmetry,[status(thm)],[89])).
% 0.96/1.12 tff(91,plain,
% 0.96/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(92,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[91])).
% 0.96/1.12 tff(93,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_yellow_0(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v2_yellow_0(A))))), ((~(v2_yellow_0(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v2_yellow_0(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v2_yellow_0(A))))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)))), ((~(v2_yellow_0(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A))))), rewrite((v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))) <=> (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))), (((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> (((~l1_orders_2(A)) | (~v2_yellow_0(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))))), rewrite((((~l1_orders_2(A)) | (~v2_yellow_0(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))), (((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(94,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[93])).
% 0.96/1.12 tff(95,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(96,plain,
% 0.96/1.12 (^[A: $i] : rewrite(((v2_yellow_0(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(97,plain,
% 0.96/1.12 (![A: $i] : ((v2_yellow_0(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[96])).
% 0.96/1.12 tff(98,axiom,(![A: $i] : ((v2_yellow_0(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc10_yellow_7')).
% 0.96/1.12 tff(99,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.96/1.12 tff(100,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.96/1.12 tff(101,plain,(
% 0.96/1.12 ![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 0.96/1.12 inference(skolemize,[status(sab)],[100])).
% 0.96/1.12 tff(102,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.96/1.12 tff(103,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.96/1.12 tff(104,plain,
% 0.96/1.12 (v2_yellow_0(A!0)),
% 0.96/1.12 inference(and_elim,[status(thm)],[19])).
% 0.96/1.12 tff(105,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(106,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(quant_inst,[status(thm)],[])).
% 0.96/1.12 tff(107,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0)))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.96/1.12 tff(108,plain,
% 0.96/1.12 (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[107, 104, 20, 103])).
% 0.96/1.12 tff(109,plain,
% 0.96/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0)))) | v1_yellow_0(k7_lattice3(A!0))),
% 0.96/1.12 inference(tautology,[status(thm)],[])).
% 0.96/1.12 tff(110,plain,
% 0.96/1.12 (v1_yellow_0(k7_lattice3(A!0))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.96/1.12 tff(111,plain,
% 0.96/1.12 (v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[110, 90])).
% 0.96/1.12 tff(112,plain,
% 0.96/1.12 (v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v1_lattice3(k7_lattice3(A!0))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[67])).
% 0.96/1.12 tff(113,plain,
% 0.96/1.12 (v1_lattice3(k7_lattice3(A!0)) <=> v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(symmetry,[status(thm)],[112])).
% 0.96/1.12 tff(114,plain,
% 0.96/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(115,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[114])).
% 0.96/1.12 tff(116,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_lattice3(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v2_lattice3(A))))), ((~(v2_lattice3(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v2_lattice3(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v2_lattice3(A))))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)))), ((~(v2_lattice3(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A))))), rewrite(((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))) <=> (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))), (((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> (((~l1_orders_2(A)) | (~v2_lattice3(A))) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))))), rewrite((((~l1_orders_2(A)) | (~v2_lattice3(A))) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))), (((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(117,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[116])).
% 0.96/1.12 tff(118,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(119,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A))) <=> ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))), (((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A)))) <=> ((v2_lattice3(A) & l1_orders_2(A)) => ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))))), rewrite(((v2_lattice3(A) & l1_orders_2(A)) => ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))), (((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A)))) <=> ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(120,plain,
% 0.96/1.12 (![A: $i] : ((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[119])).
% 0.96/1.12 tff(121,axiom,(![A: $i] : ((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc5_yellow_7')).
% 0.96/1.12 tff(122,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.96/1.12 tff(123,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.96/1.12 tff(124,plain,(
% 0.96/1.12 ![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 0.96/1.12 inference(skolemize,[status(sab)],[123])).
% 0.96/1.12 tff(125,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.96/1.12 tff(126,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.96/1.12 tff(127,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(128,plain,
% 0.96/1.12 (((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0)))))) <=> ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(129,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0)))))))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[128])).
% 0.96/1.12 tff(130,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(transitivity,[status(thm)],[129, 127])).
% 0.96/1.12 tff(131,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(quant_inst,[status(thm)],[])).
% 0.96/1.12 tff(132,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0)))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.96/1.12 tff(133,plain,
% 0.96/1.12 (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[132, 21, 20, 126])).
% 0.96/1.12 tff(134,plain,
% 0.96/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0)))) | v1_lattice3(k7_lattice3(A!0))),
% 0.96/1.12 inference(tautology,[status(thm)],[])).
% 0.96/1.12 tff(135,plain,
% 0.96/1.12 (v1_lattice3(k7_lattice3(A!0))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.96/1.12 tff(136,plain,
% 0.96/1.12 (v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[135, 113])).
% 0.96/1.12 tff(137,plain,
% 0.96/1.12 (v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v4_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[67])).
% 0.96/1.12 tff(138,plain,
% 0.96/1.12 (v4_orders_2(k7_lattice3(A!0)) <=> v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(symmetry,[status(thm)],[137])).
% 0.96/1.12 tff(139,plain,
% 0.96/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(140,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[139])).
% 0.96/1.12 tff(141,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), rewrite((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))) <=> (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> (((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))))), rewrite((((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(142,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[141])).
% 0.96/1.12 tff(143,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(144,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)))), trans(monotonicity(rewrite(((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) <=> (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)))), ((((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))) <=> ((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))))), rewrite(((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))) <=> (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))), ((((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))) <=> (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A)))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(145,plain,
% 0.96/1.12 (![A: $i] : ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[144])).
% 0.96/1.12 tff(146,axiom,(![A: $i] : ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc5_lattice3')).
% 0.96/1.12 tff(147,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.96/1.12 tff(148,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.96/1.12 tff(149,plain,(
% 0.96/1.12 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(skolemize,[status(sab)],[148])).
% 0.96/1.12 tff(150,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.96/1.12 tff(151,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[150, 140])).
% 0.96/1.12 tff(152,plain,
% 0.96/1.12 (v4_orders_2(A!0)),
% 0.96/1.12 inference(and_elim,[status(thm)],[19])).
% 0.96/1.12 tff(153,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(154,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(quant_inst,[status(thm)],[])).
% 0.96/1.12 tff(155,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.96/1.12 tff(156,plain,
% 0.96/1.12 (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[155, 43, 42, 152, 20, 151])).
% 0.96/1.12 tff(157,plain,
% 0.96/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))) | v4_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(tautology,[status(thm)],[])).
% 0.96/1.12 tff(158,plain,
% 0.96/1.12 (v4_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.96/1.12 tff(159,plain,
% 0.96/1.12 (v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[158, 138])).
% 0.96/1.12 tff(160,plain,
% 0.96/1.12 (v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v3_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[67])).
% 0.96/1.12 tff(161,plain,
% 0.96/1.12 (v3_orders_2(k7_lattice3(A!0)) <=> v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(symmetry,[status(thm)],[160])).
% 0.96/1.12 tff(162,plain,
% 0.96/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))) | v3_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(tautology,[status(thm)],[])).
% 0.96/1.12 tff(163,plain,
% 0.96/1.12 (v3_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[162, 156])).
% 0.96/1.12 tff(164,plain,
% 0.96/1.12 (v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[163, 161])).
% 0.96/1.12 tff(165,plain,
% 0.96/1.12 (v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v2_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[67])).
% 0.96/1.12 tff(166,plain,
% 0.96/1.12 (v2_orders_2(k7_lattice3(A!0)) <=> v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(symmetry,[status(thm)],[165])).
% 0.96/1.12 tff(167,plain,
% 0.96/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))) | v2_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(tautology,[status(thm)],[])).
% 0.96/1.12 tff(168,plain,
% 0.96/1.12 (v2_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[167, 156])).
% 0.96/1.12 tff(169,plain,
% 0.96/1.12 (v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.96/1.12 tff(170,plain,
% 0.96/1.12 (l1_orders_2(k7_lattice3(A!0)) <=> l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[66])).
% 0.96/1.12 tff(171,plain,
% 0.96/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(172,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[171])).
% 0.96/1.12 tff(173,plain,
% 0.96/1.12 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(174,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[173])).
% 0.96/1.12 tff(175,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(176,plain,
% 0.96/1.12 (^[A: $i] : rewrite((l1_orders_2(A) => (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(177,plain,
% 0.96/1.12 (![A: $i] : (l1_orders_2(A) => (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[176])).
% 0.96/1.12 tff(178,axiom,(![A: $i] : (l1_orders_2(A) => (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_lattice3')).
% 0.96/1.12 tff(179,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.96/1.12 tff(180,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.96/1.12 tff(181,plain,(
% 0.96/1.12 ![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 0.96/1.12 inference(skolemize,[status(sab)],[180])).
% 0.96/1.12 tff(182,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.96/1.12 tff(183,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.96/1.12 tff(184,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(185,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))))),
% 0.96/1.12 inference(quant_inst,[status(thm)],[])).
% 0.96/1.12 tff(186,plain,
% 0.96/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0)))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.96/1.12 tff(187,plain,
% 0.96/1.12 (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[186, 20, 183])).
% 0.96/1.12 tff(188,plain,
% 0.96/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0)))) | l1_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(tautology,[status(thm)],[])).
% 0.96/1.12 tff(189,plain,
% 0.96/1.12 (l1_orders_2(k7_lattice3(A!0))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.96/1.12 tff(190,plain,
% 0.96/1.12 (l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[189, 170])).
% 0.96/1.12 tff(191,plain,
% 0.96/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(192,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[191])).
% 0.96/1.12 tff(193,plain,
% 0.96/1.12 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(194,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[193])).
% 0.96/1.12 tff(195,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 0.96/1.12 inference(transitivity,[status(thm)],[194, 192])).
% 0.96/1.12 tff(196,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) <=> (~(v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) <=> (~(~(v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) <=> (v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))), ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) <=> (v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), (((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ((v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), rewrite(((v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))), (((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> (((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))), rewrite((((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(197,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[196])).
% 0.96/1.12 tff(198,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(199,plain,
% 0.96/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v1_yellow_0(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v1_yellow_0(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A)))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) <=> ((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))), (((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> (((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), rewrite((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))), (((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))))), (![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))))),
% 0.96/1.12 inference(bind,[status(th)],[])).
% 0.96/1.12 tff(200,plain,
% 0.96/1.12 (![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 0.96/1.12 inference(quant_intro,[status(thm)],[199])).
% 0.96/1.12 tff(201,axiom,(![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9_waybel13')).
% 0.96/1.12 tff(202,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.96/1.12 tff(203,plain,
% 0.96/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.96/1.12 tff(204,plain,(
% 0.96/1.12 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 0.96/1.12 inference(skolemize,[status(sab)],[203])).
% 0.96/1.12 tff(205,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.96/1.12 tff(206,plain,
% 0.96/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[205, 195])).
% 0.96/1.12 tff(207,plain,
% 0.96/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(208,plain,
% 0.96/1.12 (((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) <=> ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(209,plain,
% 0.96/1.13 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[208])).
% 0.96/1.13 tff(210,plain,
% 0.96/1.13 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[209, 207])).
% 0.96/1.13 tff(211,plain,
% 0.96/1.13 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(212,plain,
% 0.96/1.13 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.96/1.13 tff(213,plain,
% 0.96/1.13 (![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[212, 206, 190, 169, 164, 159, 136, 111])).
% 0.96/1.13 tff(214,plain,
% 0.96/1.13 (~v1_xboole_0(B!1)),
% 0.96/1.13 inference(and_elim,[status(thm)],[76])).
% 0.96/1.13 tff(215,plain,
% 0.96/1.13 (((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | (v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(216,plain,
% 0.96/1.13 ((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | (v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(217,plain,
% 0.96/1.13 ((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.96/1.14 tff(218,plain,
% 0.96/1.14 ((k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[217, 214, 213])).
% 0.96/1.14 tff(219,plain,
% 0.96/1.14 ($false),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[218, 88, 82, 78])).
% 0.96/1.14 % SZS output end Proof
% 0.96/1.14 % E exiting
%------------------------------------------------------------------------------