%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT327+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:14:22 AM UTC 2025
% Result : Theorem 2.15s 2.38s
% Output : Proof 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT327+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 20:21:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.15/2.38 % SZS status Theorem
% 2.15/2.38 % SZS output start Proof
% 2.15/2.38 tff(r3_lattices_type, type, (
% 2.15/2.38 r3_lattices: ( $i * $i * $i ) > $o)).
% 2.15/2.38 tff(tptp_fun_B_1_type, type, (
% 2.15/2.38 tptp_fun_B_1: $i)).
% 2.15/2.38 tff(tptp_fun_A_0_type, type, (
% 2.15/2.38 tptp_fun_A_0: $i)).
% 2.15/2.38 tff(tptp_fun_C_2_type, type, (
% 2.15/2.38 tptp_fun_C_2: $i)).
% 2.15/2.38 tff(r2_hidden_type, type, (
% 2.15/2.38 r2_hidden: ( $i * $i ) > $o)).
% 2.15/2.38 tff(k22_filter_2_type, type, (
% 2.15/2.38 k22_filter_2: ( $i * $i * $i ) > $i)).
% 2.15/2.38 tff(v9_lattices_type, type, (
% 2.15/2.38 v9_lattices: $i > $o)).
% 2.15/2.38 tff(v8_lattices_type, type, (
% 2.15/2.38 v8_lattices: $i > $o)).
% 2.15/2.38 tff(v7_lattices_type, type, (
% 2.15/2.38 v7_lattices: $i > $o)).
% 2.15/2.38 tff(v6_lattices_type, type, (
% 2.15/2.38 v6_lattices: $i > $o)).
% 2.15/2.38 tff(v5_lattices_type, type, (
% 2.15/2.38 v5_lattices: $i > $o)).
% 2.15/2.38 tff(v4_lattices_type, type, (
% 2.15/2.38 v4_lattices: $i > $o)).
% 2.15/2.38 tff(v3_struct_0_type, type, (
% 2.15/2.38 v3_struct_0: $i > $o)).
% 2.15/2.38 tff(v10_lattices_type, type, (
% 2.15/2.38 v10_lattices: $i > $o)).
% 2.15/2.38 tff(l3_lattices_type, type, (
% 2.15/2.38 l3_lattices: $i > $o)).
% 2.15/2.38 tff(m1_subset_1_type, type, (
% 2.15/2.38 m1_subset_1: ( $i * $i ) > $o)).
% 2.15/2.38 tff(u1_struct_0_type, type, (
% 2.15/2.38 u1_struct_0: $i > $i)).
% 2.15/2.38 tff(1,assumption,(~r3_lattices(A!0, C!2, C!2)), introduced(assumption)).
% 2.15/2.38 tff(2,plain,
% 2.15/2.38 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(3,plain,
% 2.15/2.38 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[2])).
% 2.15/2.38 tff(4,plain,
% 2.15/2.38 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~l3_lattices(A)) | (v3_struct_0(A) | (~v10_lattices(A)))))), rewrite(((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~l3_lattices(A)) | (v3_struct_0(A) | (~v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(5,plain,
% 2.15/2.38 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[4])).
% 2.15/2.38 tff(6,plain,
% 2.15/2.38 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(7,plain,
% 2.15/2.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(8,plain,
% 2.15/2.38 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[7])).
% 2.15/2.38 tff(9,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 2.15/2.38 tff(10,plain,
% 2.15/2.38 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 2.15/2.38 tff(11,plain,
% 2.15/2.38 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 2.15/2.38 tff(12,plain,(
% 2.15/2.38 ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 2.15/2.38 inference(skolemize,[status(sab)],[11])).
% 2.15/2.38 tff(13,plain,
% 2.15/2.38 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 2.15/2.38 tff(14,plain,
% 2.15/2.38 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[13, 3])).
% 2.15/2.38 tff(15,plain,
% 2.15/2.38 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(16,plain,
% 2.15/2.38 ((~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(17,plain,
% 2.15/2.38 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[16])).
% 2.15/2.38 tff(18,plain,
% 2.15/2.38 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[17])).
% 2.15/2.38 tff(19,plain,
% 2.15/2.38 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[18, 15])).
% 2.15/2.38 tff(20,plain,
% 2.15/2.38 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(21,plain,
% 2.15/2.38 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(22,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t64_filter_2')).
% 2.15/2.38 tff(23,plain,
% 2.15/2.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 2.15/2.38 tff(24,plain,
% 2.15/2.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[23, 20])).
% 2.15/2.38 tff(25,plain,
% 2.15/2.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 2.15/2.38 tff(26,plain,
% 2.15/2.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((r2_hidden(B, k22_filter_2(A, B, C)) & r2_hidden(C, k22_filter_2(A, B, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[25, 20])).
% 2.15/2.38 tff(27,plain,
% 2.15/2.38 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 2.15/2.38 tff(28,plain,
% 2.15/2.38 (l3_lattices(A!0)),
% 2.15/2.38 inference(and_elim,[status(thm)],[27])).
% 2.15/2.38 tff(29,plain,
% 2.15/2.38 (v10_lattices(A!0)),
% 2.15/2.38 inference(and_elim,[status(thm)],[27])).
% 2.15/2.38 tff(30,plain,
% 2.15/2.38 (~v3_struct_0(A!0)),
% 2.15/2.38 inference(and_elim,[status(thm)],[27])).
% 2.15/2.38 tff(31,plain,
% 2.15/2.38 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(32,plain,
% 2.15/2.38 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(33,plain,
% 2.15/2.38 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.15/2.38 tff(34,plain,
% 2.15/2.38 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[33, 30, 29, 28, 14])).
% 2.15/2.38 tff(35,plain,
% 2.15/2.38 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v9_lattices(A!0)),
% 2.15/2.38 inference(tautology,[status(thm)],[])).
% 2.15/2.38 tff(36,plain,
% 2.15/2.38 (v9_lattices(A!0)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 2.15/2.38 tff(37,plain,
% 2.15/2.38 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v8_lattices(A!0)),
% 2.15/2.38 inference(tautology,[status(thm)],[])).
% 2.15/2.38 tff(38,plain,
% 2.15/2.38 (v8_lattices(A!0)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[37, 34])).
% 2.15/2.38 tff(39,plain,
% 2.15/2.38 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 2.15/2.38 inference(tautology,[status(thm)],[])).
% 2.15/2.38 tff(40,plain,
% 2.15/2.38 (v6_lattices(A!0)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[39, 34])).
% 2.15/2.38 tff(41,plain,
% 2.15/2.38 (^[A: $i, B: $i, C: $i] : refl((r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(42,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[41])).
% 2.15/2.38 tff(43,plain,
% 2.15/2.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | r3_lattices(A, B, B)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(44,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[43])).
% 2.15/2.38 tff(45,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(46,plain,
% 2.15/2.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(47,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[46])).
% 2.15/2.38 tff(48,axiom,(![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r3_lattices')).
% 2.15/2.38 tff(49,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 2.15/2.38 tff(50,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[49, 45])).
% 2.15/2.38 tff(51,plain,(
% 2.15/2.38 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 2.15/2.38 inference(skolemize,[status(sab)],[50])).
% 2.15/2.38 tff(52,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[51, 44])).
% 2.15/2.38 tff(53,plain,
% 2.15/2.38 (![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[52, 42])).
% 2.15/2.38 tff(54,plain,
% 2.15/2.38 (~((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 2.15/2.38 inference(and_elim,[status(thm)],[27])).
% 2.15/2.38 tff(55,plain,
% 2.15/2.38 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 2.15/2.38 inference(or_elim,[status(thm)],[54])).
% 2.15/2.38 tff(56,plain,
% 2.15/2.38 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 2.15/2.38 inference(and_elim,[status(thm)],[27])).
% 2.15/2.38 tff(57,plain,
% 2.15/2.38 (((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, C!2, C!2))) <=> ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, C!2, C!2))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(58,plain,
% 2.15/2.38 ((r3_lattices(A!0, C!2, C!2) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, C!2, C!2))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(59,plain,
% 2.15/2.38 (((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (r3_lattices(A!0, C!2, C!2) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, C!2, C!2)))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[58])).
% 2.15/2.38 tff(60,plain,
% 2.15/2.38 (((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (r3_lattices(A!0, C!2, C!2) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, C!2, C!2))),
% 2.15/2.38 inference(transitivity,[status(thm)],[59, 57])).
% 2.15/2.38 tff(61,plain,
% 2.15/2.38 ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (r3_lattices(A!0, C!2, C!2) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(62,plain,
% 2.15/2.38 ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, C!2, C!2)),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 2.15/2.38 tff(63,plain,
% 2.15/2.38 ($false),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[62, 30, 28, 56, 55, 53, 40, 38, 36, 1])).
% 2.15/2.38 tff(64,plain,(r3_lattices(A!0, C!2, C!2)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.38 tff(65,plain,
% 2.15/2.38 (r3_lattices(A!0, B!1, C!2)),
% 2.15/2.38 inference(or_elim,[status(thm)],[54])).
% 2.15/2.38 tff(66,plain,
% 2.15/2.38 ((~((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2)))) | (~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))),
% 2.15/2.38 inference(tautology,[status(thm)],[])).
% 2.15/2.38 tff(67,plain,
% 2.15/2.38 ((~((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2)))) | (~r3_lattices(A!0, C!2, C!2))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[66, 65])).
% 2.15/2.38 tff(68,plain,
% 2.15/2.38 (~((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2)))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[67, 64])).
% 2.15/2.38 tff(69,plain,
% 2.15/2.38 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(70,plain,
% 2.15/2.38 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[69])).
% 2.15/2.38 tff(71,plain,
% 2.15/2.38 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(72,plain,
% 2.15/2.38 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[71])).
% 2.15/2.38 tff(73,plain,
% 2.15/2.38 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[72, 70])).
% 2.15/2.38 tff(74,plain,
% 2.15/2.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))))),
% 2.15/2.38 inference(bind,[status(th)],[])).
% 2.15/2.38 tff(75,plain,
% 2.15/2.38 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 2.15/2.38 inference(quant_intro,[status(thm)],[74])).
% 2.15/2.38 tff(76,plain,
% 2.15/2.38 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(77,plain,
% 2.15/2.38 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))) <=> ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))))),
% 2.15/2.39 inference(bind,[status(th)],[])).
% 2.15/2.39 tff(78,plain,
% 2.15/2.39 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 2.15/2.39 inference(quant_intro,[status(thm)],[77])).
% 2.15/2.39 tff(79,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_filter_2')).
% 2.15/2.39 tff(80,plain,
% 2.15/2.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.15/2.39 tff(81,plain,
% 2.15/2.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[80, 76])).
% 2.15/2.39 tff(82,plain,(
% 2.15/2.39 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 2.15/2.39 inference(skolemize,[status(sab)],[81])).
% 2.15/2.39 tff(83,plain,
% 2.15/2.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[82, 75])).
% 2.15/2.39 tff(84,plain,
% 2.15/2.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[83, 73])).
% 2.15/2.39 tff(85,plain,
% 2.15/2.39 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(86,plain,
% 2.15/2.39 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(87,plain,
% 2.15/2.39 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 2.15/2.39 tff(88,plain,
% 2.15/2.39 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[87, 30, 29, 28, 84])).
% 2.15/2.39 tff(89,plain,
% 2.15/2.39 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C)))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(90,plain,
% 2.15/2.39 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C)))))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(91,plain,
% 2.15/2.39 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.15/2.39 tff(92,plain,
% 2.15/2.39 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[91, 56, 88])).
% 2.15/2.39 tff(93,plain,
% 2.15/2.39 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(94,plain,
% 2.15/2.39 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2))))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(95,plain,
% 2.15/2.39 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.15/2.39 tff(96,plain,
% 2.15/2.39 (![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[95, 55, 92])).
% 2.15/2.39 tff(97,plain,
% 2.15/2.39 (((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) <=> r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))))) <=> ((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) <=> r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(98,plain,
% 2.15/2.39 ((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) <=> r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(99,plain,
% 2.15/2.39 ((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) <=> r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.15/2.39 tff(100,plain,
% 2.15/2.39 (~(((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) <=> r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[99, 65, 55, 96])).
% 2.15/2.39 tff(101,plain,
% 2.15/2.39 ((((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) <=> r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) | ((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) | r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))),
% 2.15/2.39 inference(tautology,[status(thm)],[])).
% 2.15/2.39 tff(102,plain,
% 2.15/2.39 (((~r3_lattices(A!0, B!1, C!2)) | (~r3_lattices(A!0, C!2, C!2))) | r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[101, 100])).
% 2.15/2.39 tff(103,plain,
% 2.15/2.39 (r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[102, 68])).
% 2.15/2.39 tff(104,plain,
% 2.15/2.39 ((~(~((~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | (~r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))))) <=> ((~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | (~r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(105,plain,
% 2.15/2.39 ((r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))) <=> (~((~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | (~r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(106,plain,
% 2.15/2.39 ((~(r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))) <=> (~(~((~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | (~r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[105])).
% 2.15/2.39 tff(107,plain,
% 2.15/2.39 ((~(r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))) <=> ((~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | (~r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2))))),
% 2.15/2.39 inference(transitivity,[status(thm)],[106, 104])).
% 2.15/2.39 tff(108,plain,
% 2.15/2.39 (~(r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)) & r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))),
% 2.15/2.39 inference(or_elim,[status(thm)],[54])).
% 2.15/2.39 tff(109,plain,
% 2.15/2.39 ((~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | (~r2_hidden(C!2, k22_filter_2(A!0, B!1, C!2)))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 2.15/2.39 tff(110,plain,
% 2.15/2.39 (~r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[109, 103])).
% 2.15/2.39 tff(111,plain,
% 2.15/2.39 (((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) <=> r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)))))) <=> ((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) <=> r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(112,plain,
% 2.15/2.39 ((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) <=> r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(113,plain,
% 2.15/2.39 ((~![D: $i] : ((~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C!2))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) <=> r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.15/2.39 tff(114,plain,
% 2.15/2.39 (~(((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) <=> r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[113, 56, 65, 96])).
% 2.15/2.39 tff(115,plain,
% 2.15/2.39 ((((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) <=> r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))) | ((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) | r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))),
% 2.15/2.39 inference(tautology,[status(thm)],[])).
% 2.15/2.39 tff(116,plain,
% 2.15/2.39 (((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))) | r2_hidden(B!1, k22_filter_2(A!0, B!1, C!2))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[115, 114])).
% 2.15/2.39 tff(117,plain,
% 2.15/2.39 ((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[116, 110])).
% 2.15/2.39 tff(118,plain,
% 2.15/2.39 ((~((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2)))) | (~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2))),
% 2.15/2.39 inference(tautology,[status(thm)],[])).
% 2.15/2.39 tff(119,plain,
% 2.15/2.39 ((~((~r3_lattices(A!0, B!1, B!1)) | (~r3_lattices(A!0, B!1, C!2)))) | (~r3_lattices(A!0, B!1, B!1))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[118, 65])).
% 2.15/2.39 tff(120,plain,
% 2.15/2.39 (~r3_lattices(A!0, B!1, B!1)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[119, 117])).
% 2.15/2.39 tff(121,plain,
% 2.15/2.39 (((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1))) <=> ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(122,plain,
% 2.15/2.39 ((r3_lattices(A!0, B!1, B!1) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(123,plain,
% 2.15/2.39 (((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (r3_lattices(A!0, B!1, B!1) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1)))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[122])).
% 2.15/2.39 tff(124,plain,
% 2.15/2.39 (((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (r3_lattices(A!0, B!1, B!1) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1))),
% 2.15/2.39 inference(transitivity,[status(thm)],[123, 121])).
% 2.15/2.39 tff(125,plain,
% 2.15/2.39 ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (r3_lattices(A!0, B!1, B!1) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(126,plain,
% 2.15/2.39 ((~![A: $i, B: $i, C: $i] : (r3_lattices(A, B, B) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 2.24/2.41 tff(127,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[126, 30, 28, 56, 53, 40, 38, 36, 120])).
% 2.24/2.41 % SZS output end Proof
% 2.24/2.41 % E exiting
%------------------------------------------------------------------------------