%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU411+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 05:27:50 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU411+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:07:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(v1_xboole_0_type, type, (
% 0.19/0.43 v1_xboole_0: $i > $o)).
% 0.19/0.43 tff(k1_xboole_0_type, type, (
% 0.19/0.43 k1_xboole_0: $i)).
% 0.19/0.43 tff(k3_xboole_0_type, type, (
% 0.19/0.43 k3_xboole_0: ( $i * $i ) > $i)).
% 0.19/0.43 tff(u1_struct_0_type, type, (
% 0.19/0.43 u1_struct_0: $i > $i)).
% 0.19/0.43 tff(tptp_fun_B_1_type, type, (
% 0.19/0.43 tptp_fun_B_1: $i)).
% 0.19/0.43 tff(tptp_fun_A_0_type, type, (
% 0.19/0.43 tptp_fun_A_0: $i)).
% 0.19/0.43 tff(r2_hidden_type, type, (
% 0.19/0.43 r2_hidden: ( $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_B_4_type, type, (
% 0.19/0.43 tptp_fun_B_4: $i > $i)).
% 0.19/0.43 tff(r1_orders_2_type, type, (
% 0.19/0.43 r1_orders_2: ( $i * $i * $i ) > $o)).
% 0.19/0.43 tff(k3_yellow_0_type, type, (
% 0.19/0.43 k3_yellow_0: $i > $i)).
% 0.19/0.43 tff(m1_subset_1_type, type, (
% 0.19/0.43 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.43 tff(l1_orders_2_type, type, (
% 0.19/0.43 l1_orders_2: $i > $o)).
% 0.19/0.43 tff(v3_struct_0_type, type, (
% 0.19/0.43 v3_struct_0: $i > $o)).
% 0.19/0.43 tff(v1_lattice3_type, type, (
% 0.19/0.43 v1_lattice3: $i > $o)).
% 0.19/0.43 tff(v1_yellow_0_type, type, (
% 0.19/0.43 v1_yellow_0: $i > $o)).
% 0.19/0.43 tff(v4_orders_2_type, type, (
% 0.19/0.43 v4_orders_2: $i > $o)).
% 0.19/0.43 tff(v3_orders_2_type, type, (
% 0.19/0.43 v3_orders_2: $i > $o)).
% 0.19/0.43 tff(v2_orders_2_type, type, (
% 0.19/0.43 v2_orders_2: $i > $o)).
% 0.19/0.43 tff(k1_zfmisc_1_type, type, (
% 0.19/0.43 k1_zfmisc_1: $i > $i)).
% 0.19/0.43 tff(v12_waybel_0_type, type, (
% 0.19/0.43 v12_waybel_0: ( $i * $i ) > $o)).
% 0.19/0.43 tff(v1_waybel_0_type, type, (
% 0.19/0.43 v1_waybel_0: ( $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_C_2_type, type, (
% 0.19/0.43 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_D_3_type, type, (
% 0.19/0.43 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.19/0.43 tff(l1_struct_0_type, type, (
% 0.19/0.43 l1_struct_0: $i > $o)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(4,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.43 tff(6,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.19/0.43 inference(skolemize,[status(sab)],[5])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.19/0.43 inference(symmetry,[status(thm)],[9])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.19/0.43 inference(symmetry,[status(thm)],[11])).
% 0.19/0.43 tff(13,assumption,(r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))), introduced(assumption)).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A))))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & l1_orders_2(B)) <=> (~(v3_struct_0(B) | (~l1_orders_2(B))))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (~(~(v3_struct_0(B) | (~l1_orders_2(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_orders_2(B))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (v3_struct_0(B) | (~l1_orders_2(B))))), (((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), rewrite(((v3_struct_0(B) | (~l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), (((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), (![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))) <=> ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), (![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))) <=> ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), ((((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))) <=> (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), rewrite((((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), ((((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))) <=> ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), (![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))))) <=> (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.43 tff(25,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_latsum_1')).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.43 tff(28,plain,(
% 0.19/0.43 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[27])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))) <=> ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 ((~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))) <=> (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ((((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))) <=> (((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 ((((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))) <=> ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~![A: $i] : ((((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & v1_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_yellow_0(B)) & v1_lattice3(B)) & l1_orders_2(B)) => (((((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) => r2_hidden(k3_yellow_0(B), u1_struct_0(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(37,axiom,(~![A: $i] : ((((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & v1_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_yellow_0(B)) & v1_lattice3(B)) & l1_orders_2(B)) => (((((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) => r2_hidden(k3_yellow_0(B), u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_latsum_1')).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (l1_orders_2(A!0)),
% 0.19/0.44 inference(and_elim,[status(thm)],[42])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (~v3_struct_0(A!0)),
% 0.19/0.44 inference(and_elim,[status(thm)],[42])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[47, 44, 43, 30])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))),
% 0.19/0.44 inference(and_elim,[status(thm)],[42])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 ((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)),
% 0.19/0.44 inference(or_elim,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (l1_orders_2(B!1)),
% 0.19/0.44 inference(and_elim,[status(thm)],[50])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (~v3_struct_0(B!1)),
% 0.19/0.44 inference(and_elim,[status(thm)],[50])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[55, 52, 51, 48])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1)))) | ((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))) <=> ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1)))) | ((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(C, u1_struct_0(B!1)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 ((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[60, 14])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))), ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))), ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))), (((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ((v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))), (((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) <=> ((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A))), (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> (((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A)) & l1_orders_2(A)))), rewrite((((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))), (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))), ((((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B))) <=> (((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))))), rewrite((((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))), ((((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B))) <=> ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (![A: $i] : (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.44 tff(74,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_yellow_0')).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.44 tff(77,plain,(
% 0.19/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[76])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[79, 63])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (v1_yellow_0(B!1)),
% 0.19/0.44 inference(and_elim,[status(thm)],[50])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (v4_orders_2(B!1)),
% 0.19/0.44 inference(and_elim,[status(thm)],[50])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)) | (~v1_yellow_0(B!1)) | (~v4_orders_2(B!1)) | (~l1_orders_2(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)) | (~v1_yellow_0(B!1)) | (~v4_orders_2(B!1)) | (~l1_orders_2(B!1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 ((v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) <=> (v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)) | (~v1_yellow_0(B!1)) | (~v4_orders_2(B!1)) | (~l1_orders_2(B!1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)) | (~v1_yellow_0(B!1)) | (~v4_orders_2(B!1)) | (~l1_orders_2(B!1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)) | (~v1_yellow_0(B!1)) | (~v4_orders_2(B!1)) | (~l1_orders_2(B!1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)) | (~v1_yellow_0(B!1)) | (~v4_orders_2(B!1)) | (~l1_orders_2(B!1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[88, 52, 82, 81, 51, 80])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 (r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[92, 89, 61])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) <=> v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) <=> v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)),
% 0.19/0.45 inference(symmetry,[status(thm)],[94])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 ((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.45 inference(or_elim,[status(thm)],[49])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)),
% 0.19/0.45 inference(and_elim,[status(thm)],[96])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[97, 95])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 (m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 (m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[99])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 (m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[96])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 (m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (^[A: $i] : refl(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.45 tff(109,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))) <=> (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))), ((l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))))) <=> (l1_orders_2(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))))), rewrite((l1_orders_2(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))), ((l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 (![A: $i] : (l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.45 tff(115,axiom,(![A: $i] : (l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d19_waybel_0')).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.19/0.45 tff(118,plain,(
% 0.19/0.45 ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))))))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[117])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[120, 104])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C)))))))))) <=> ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[124, 122])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[127, 51, 121])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))) <=> ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[131, 129])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 128])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[135, 102])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))) | ((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 ((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 ((~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[139, 138, 98])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) <=> ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[142])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[143, 141])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[146, 140])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[147, 61])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[151, 52, 51, 30])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 (![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[155, 44, 43, 152])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[160])).
% 0.19/0.47 tff(162,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.19/0.47 tff(165,plain,(
% 0.19/0.47 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[164])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (l1_struct_0(A!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[169, 43, 166])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[171])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[173])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.47 tff(178,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.19/0.47 tff(181,plain,(
% 0.19/0.47 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[180])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[185])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[186, 184])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[189, 44, 183, 170])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[191])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[194])).
% 0.19/0.47 tff(196,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.19/0.47 tff(199,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[198])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 (~r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0))),
% 0.19/0.47 inference(or_elim,[status(thm)],[49])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[204, 201, 200])).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[205, 190])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[209, 206, 156])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (^[A: $i] : refl(((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (^[A: $i] : rewrite((l1_orders_2(A) => m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (![A: $i] : (l1_orders_2(A) => m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[214])).
% 0.19/0.47 tff(216,axiom,(![A: $i] : (l1_orders_2(A) => m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_yellow_0')).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.19/0.47 tff(219,plain,(
% 0.19/0.47 ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[218])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | ((~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1)))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | (~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 ((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | ((~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 ((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | (~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 (m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[223, 51, 220])).
% 0.19/0.47 tff(225,plain,
% 0.19/0.47 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.47 tff(228,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[227, 224, 210, 13, 148, 93])).
% 0.19/0.47 tff(229,plain,(~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))) <=> (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(231,plain,
% 0.19/0.47 (![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))) <=> ![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[230])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (^[A: $i, B: $i] : refl((~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))) <=> (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 (![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))) <=> ![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[232])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (![A: $i] : ![B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))) <=> ![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(pull_quant,[status(thm)],[])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) <=> ![B: $i] : ((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))), ((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) <=> (~![B: $i] : ((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))), pull_quant((~![B: $i] : ((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) <=> ?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))), ((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) <=> ?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))), (((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))) <=> ((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | ?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))), pull_quant(((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | ?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))) <=> ?[B: $i] : ((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))), (((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))) <=> ?[B: $i] : ((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))), ((~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> (~?[B: $i] : ((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))))), pull_quant((~?[B: $i] : ((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))) <=> ![B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))), ((~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> ![B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> ![A: $i] : ![B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[235])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 (![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> ![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[236, 234])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> ![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[237, 233])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 (^[A: $i] : rewrite((~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 (![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> ![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[239])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 (![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))))) <=> ![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[240, 238])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (^[A: $i] : trans(monotonicity(rewrite(((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) <=> ((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))), ((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))), rewrite((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))))), ((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> ![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[242])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 (![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A))) <=> ![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(245,axiom,(![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_xboole_0')).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 (![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.48 tff(247,plain,(
% 0.19/0.48 ![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[246])).
% 0.19/0.48 tff(248,plain,
% 0.19/0.48 (![A: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.19/0.48 tff(249,plain,
% 0.19/0.48 (![A: $i, B: $i] : (~((~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) | (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.19/0.48 tff(250,plain,
% 0.19/0.48 (![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[249, 231])).
% 0.19/0.48 tff(251,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))) | (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0)) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(252,plain,
% 0.19/0.48 (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0)) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.19/0.48 tff(253,plain,
% 0.19/0.48 (((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0)) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | ((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(254,plain,
% 0.19/0.48 ((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.19/0.48 tff(255,plain,
% 0.19/0.48 ((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(256,plain,
% 0.19/0.48 ((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.19/0.48 tff(257,plain,
% 0.19/0.48 (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[256, 229])).
% 0.19/0.48 tff(258,plain,
% 0.19/0.48 (k1_xboole_0 = k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))),
% 0.19/0.48 inference(symmetry,[status(thm)],[257])).
% 0.19/0.48 tff(259,plain,
% 0.19/0.48 (k1_xboole_0 = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.19/0.48 inference(transitivity,[status(thm)],[258, 10])).
% 0.19/0.48 tff(260,plain,
% 0.19/0.48 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[259])).
% 0.19/0.48 tff(261,plain,
% 0.19/0.48 (v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> v1_xboole_0(k1_xboole_0)),
% 0.19/0.48 inference(symmetry,[status(thm)],[260])).
% 0.19/0.48 tff(262,plain,
% 0.19/0.48 ((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) <=> (~v1_xboole_0(k1_xboole_0))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[261])).
% 0.19/0.48 tff(263,plain,
% 0.19/0.48 (~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[96])).
% 0.19/0.48 tff(264,plain,
% 0.19/0.48 (~v1_xboole_0(k1_xboole_0)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.19/0.48 tff(265,plain,
% 0.19/0.48 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(266,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.19/0.48 tff(267,plain,
% 0.19/0.48 (v1_xboole_0(k1_xboole_0)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.19/0.48 tff(268,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[267, 264])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------