%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU407+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:27:49 AM UTC 2025
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU407+1 : TPTP v9.0.0. Released v3.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 07:03:25 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 tff(r2_hidden_type, type, (
% 0.22/0.44 r2_hidden: ( $i * $i ) > $o)).
% 0.22/0.44 tff(k2_xboole_0_type, type, (
% 0.22/0.44 k2_xboole_0: ( $i * $i ) > $i)).
% 0.22/0.44 tff(u1_struct_0_type, type, (
% 0.22/0.44 u1_struct_0: $i > $i)).
% 0.22/0.44 tff(tptp_fun_B_1_type, type, (
% 0.22/0.44 tptp_fun_B_1: $i)).
% 0.22/0.44 tff(tptp_fun_A_0_type, type, (
% 0.22/0.44 tptp_fun_A_0: $i)).
% 0.22/0.44 tff(tptp_fun_C_2_type, type, (
% 0.22/0.44 tptp_fun_C_2: $i)).
% 0.22/0.44 tff(k1_latsum_1_type, type, (
% 0.22/0.44 k1_latsum_1: ( $i * $i ) > $i)).
% 0.22/0.44 tff(g1_orders_2_type, type, (
% 0.22/0.44 g1_orders_2: ( $i * $i ) > $i)).
% 0.22/0.44 tff(u1_orders_2_type, type, (
% 0.22/0.44 u1_orders_2: $i > $i)).
% 0.22/0.44 tff(v1_orders_2_type, type, (
% 0.22/0.44 v1_orders_2: $i > $o)).
% 0.22/0.44 tff(v3_struct_0_type, type, (
% 0.22/0.44 v3_struct_0: $i > $o)).
% 0.22/0.44 tff(l1_orders_2_type, type, (
% 0.22/0.44 l1_orders_2: $i > $o)).
% 0.22/0.44 tff(m1_subset_1_type, type, (
% 0.22/0.44 m1_subset_1: ( $i * $i ) > $o)).
% 0.22/0.44 tff(k4_xboole_0_type, type, (
% 0.22/0.44 k4_xboole_0: ( $i * $i ) > $i)).
% 0.22/0.44 tff(k7_relset_1_type, type, (
% 0.22/0.44 k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.44 tff(v1_xboole_0_type, type, (
% 0.22/0.44 v1_xboole_0: $i > $o)).
% 0.22/0.44 tff(l1_struct_0_type, type, (
% 0.22/0.44 l1_struct_0: $i > $o)).
% 0.22/0.44 tff(tptp_fun_D_3_type, type, (
% 0.22/0.44 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.22/0.44 tff(1,plain,
% 0.22/0.44 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B)))))) <=> (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(2,plain,
% 0.22/0.44 (![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.44 tff(3,plain,
% 0.22/0.44 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B)) <=> (~(v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A))))), ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)))), ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) <=> (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A))))), rewrite(((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))) <=> (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> ((v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A))) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B)))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A))) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B)))))) <=> (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))), (((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(4,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.44 tff(5,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(6,plain,
% 0.22/0.44 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) & l1_orders_2(B)) <=> ((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))), (((((~v3_struct_0(A)) & l1_orders_2(A)) & l1_orders_2(B)) => ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> (((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B)) => ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B)) => ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))), (((((~v3_struct_0(A)) & l1_orders_2(A)) & l1_orders_2(B)) => ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(7,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_orders_2(A)) & l1_orders_2(B)) => ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.44 tff(8,axiom,(![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_orders_2(A)) & l1_orders_2(B)) => ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_latsum_1')).
% 0.22/0.44 tff(9,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.44 tff(10,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.44 tff(11,plain,(
% 0.22/0.44 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A) & l1_orders_2(B))) | ((~v3_struct_0(k1_latsum_1(A, B))) & v1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[10])).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.44 tff(13,plain,
% 0.22/0.44 (![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.22/0.44 tff(14,plain,
% 0.22/0.44 ((((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> ((~v3_struct_0(A!0)) & l1_orders_2(A!0) & (~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 ((((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))))) <=> ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 ((~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))) <=> (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 ((((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))))) <=> (((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[16])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 ((((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))))) <=> ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[17, 15])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 ((((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & (((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> (((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 ((((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & (((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))) <=> ((~v3_struct_0(A!0)) & l1_orders_2(A!0) & (~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[19, 14])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 ((~![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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, 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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B))))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(22,plain,
% 0.22/0.44 ((~![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B))) => (r2_hidden(C, u1_struct_0(A)) | r2_hidden(C, k4_xboole_0(u1_struct_0(B), u1_struct_0(A)))))))) <=> (~![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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B))))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(23,axiom,(~![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B))) => (r2_hidden(C, u1_struct_0(A)) | r2_hidden(C, k4_xboole_0(u1_struct_0(B), u1_struct_0(A)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_latsum_1')).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (~![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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (~![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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 (~![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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 (~![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, k4_xboole_0(u1_struct_0(B), u1_struct_0(A))) | r2_hidden(C, u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(k1_latsum_1(A, B)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 ((~v3_struct_0(A!0)) & l1_orders_2(A!0) & (~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 (l1_orders_2(B!1)),
% 0.22/0.44 inference(and_elim,[status(thm)],[28])).
% 0.22/0.44 tff(30,plain,
% 0.22/0.44 (l1_orders_2(A!0)),
% 0.22/0.44 inference(and_elim,[status(thm)],[28])).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (~v3_struct_0(A!0)),
% 0.22/0.44 inference(and_elim,[status(thm)],[28])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))) | (v3_struct_0(A!0) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~(v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))) | v3_struct_0(A!0) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~(v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))) | (v3_struct_0(A!0) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~(v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~l1_orders_2(B)) | (~l1_orders_2(A)) | (~(v3_struct_0(k1_latsum_1(A, B)) | (~v1_orders_2(k1_latsum_1(A, B))))))) | v3_struct_0(A!0) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~(v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 (~(v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[34, 31, 30, 29, 13])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 ((v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))) | v1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 (v1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.44 tff(38,plain,
% 0.22/0.44 (^[A: $i, B: $i] : refl(((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(39,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))) <=> ![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.45 tff(40,plain,
% 0.22/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_orders_2(A) & l1_orders_2(B)) <=> (~((~l1_orders_2(B)) | (~l1_orders_2(A))))), ((~(l1_orders_2(A) & l1_orders_2(B))) <=> (~(~((~l1_orders_2(B)) | (~l1_orders_2(A))))))), rewrite((~(~((~l1_orders_2(B)) | (~l1_orders_2(A))))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)))), ((~(l1_orders_2(A) & l1_orders_2(B))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A))))), rewrite((v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))) <=> (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))), (((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> (((~l1_orders_2(B)) | (~l1_orders_2(A))) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))))), rewrite((((~l1_orders_2(B)) | (~l1_orders_2(A))) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B)))))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))), (((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(41,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.45 tff(42,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(43,plain,
% 0.22/0.45 (^[A: $i, B: $i] : rewrite(((l1_orders_2(A) & l1_orders_2(B)) => (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(44,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((l1_orders_2(A) & l1_orders_2(B)) => (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B)))) <=> ![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.45 tff(45,axiom,(![A: $i, B: $i] : ((l1_orders_2(A) & l1_orders_2(B)) => (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_latsum_1')).
% 0.22/0.45 tff(46,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.45 tff(47,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.22/0.45 tff(48,plain,(
% 0.22/0.45 ![A: $i, B: $i] : ((~(l1_orders_2(A) & l1_orders_2(B))) | (v1_orders_2(k1_latsum_1(A, B)) & l1_orders_2(k1_latsum_1(A, B))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[47])).
% 0.22/0.45 tff(49,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.22/0.45 tff(51,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 ((~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))) <=> (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 (((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[53])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1)))))) <=> ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[54, 52])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[55])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[56, 51])).
% 0.22/0.45 tff(58,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | ((~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(59,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : ((~l1_orders_2(B)) | (~l1_orders_2(A)) | (~((~v1_orders_2(k1_latsum_1(A, B))) | (~l1_orders_2(k1_latsum_1(A, B))))))) | (~l1_orders_2(B!1)) | (~l1_orders_2(A!0)) | (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.45 tff(60,plain,
% 0.22/0.45 (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[59, 30, 29, 50])).
% 0.22/0.45 tff(61,plain,
% 0.22/0.45 (((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))) | l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(62,plain,
% 0.22/0.45 (l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.22/0.45 tff(63,plain,
% 0.22/0.45 (^[A: $i] : refl(((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A))) <=> ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(64,plain,
% 0.22/0.45 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A))) <=> ![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.22/0.45 tff(65,plain,
% 0.22/0.45 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A))) <=> ![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(66,plain,
% 0.22/0.45 (^[A: $i] : trans(monotonicity(rewrite((v1_orders_2(A) => (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) <=> ((~v1_orders_2(A)) | (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))))), ((l1_orders_2(A) => (v1_orders_2(A) => (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))))) <=> (l1_orders_2(A) => ((~v1_orders_2(A)) | (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))))))), rewrite((l1_orders_2(A) => ((~v1_orders_2(A)) | (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))))) <=> ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))), ((l1_orders_2(A) => (v1_orders_2(A) => (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))))) <=> ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(67,plain,
% 0.22/0.45 (![A: $i] : (l1_orders_2(A) => (v1_orders_2(A) => (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.22/0.45 tff(68,axiom,(![A: $i] : (l1_orders_2(A) => (v1_orders_2(A) => (A = g1_orders_2(u1_struct_0(A), u1_orders_2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 0.22/0.45 tff(69,plain,
% 0.22/0.45 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.45 tff(70,plain,
% 0.22/0.45 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.22/0.45 tff(71,plain,(
% 0.22/0.45 ![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[70])).
% 0.22/0.45 tff(72,plain,
% 0.22/0.45 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.22/0.45 tff(73,plain,
% 0.22/0.45 (((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))) <=> ((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(74,plain,
% 0.22/0.45 (((k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1)))) <=> ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(75,plain,
% 0.22/0.45 (((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | ((k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))) <=> ((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[74])).
% 0.22/0.45 tff(76,plain,
% 0.22/0.45 (((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | ((k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))) <=> ((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[75, 73])).
% 0.22/0.45 tff(77,plain,
% 0.22/0.45 ((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | ((k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(78,plain,
% 0.22/0.45 ((~![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))) | (~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.22/0.45 tff(79,plain,
% 0.22/0.45 ((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[78, 72])).
% 0.22/0.45 tff(80,plain,
% 0.22/0.45 (k1_latsum_1(A!0, B!1) = g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[79, 62, 37])).
% 0.22/0.45 tff(81,plain,
% 0.22/0.45 (u1_struct_0(k1_latsum_1(A!0, B!1)) = u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[80])).
% 0.22/0.45 tff(82,plain,
% 0.22/0.45 (u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = u1_struct_0(k1_latsum_1(A!0, B!1))),
% 0.22/0.45 inference(symmetry,[status(thm)],[81])).
% 0.22/0.45 tff(83,plain,
% 0.22/0.45 (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)),
% 0.22/0.45 inference(symmetry,[status(thm)],[80])).
% 0.22/0.45 tff(84,plain,
% 0.22/0.45 (v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) <=> v1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[83])).
% 0.22/0.45 tff(85,plain,
% 0.22/0.45 (v1_orders_2(k1_latsum_1(A!0, B!1)) <=> v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(symmetry,[status(thm)],[84])).
% 0.22/0.45 tff(86,plain,
% 0.22/0.45 (v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[37, 85])).
% 0.22/0.45 tff(87,plain,
% 0.22/0.45 (l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) <=> l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[83])).
% 0.22/0.45 tff(88,plain,
% 0.22/0.45 (l1_orders_2(k1_latsum_1(A!0, B!1)) <=> l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(symmetry,[status(thm)],[87])).
% 0.22/0.45 tff(89,plain,
% 0.22/0.45 (l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[62, 88])).
% 0.22/0.45 tff(90,plain,
% 0.22/0.45 (^[A: $i] : refl(((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(91,plain,
% 0.22/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[90])).
% 0.22/0.45 tff(92,plain,
% 0.22/0.45 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(93,plain,
% 0.22/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[92])).
% 0.22/0.45 tff(94,plain,
% 0.22/0.45 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[93, 91])).
% 0.22/0.46 tff(95,plain,
% 0.22/0.46 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(96,plain,
% 0.22/0.46 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[95])).
% 0.22/0.46 tff(97,plain,
% 0.22/0.46 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(98,plain,
% 0.22/0.46 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))) <=> ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))), (![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))) <=> ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))), ((l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))) <=> (l1_orders_2(B) => ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))), rewrite((l1_orders_2(B) => ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))) <=> ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))), ((l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))) <=> ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))))), (![B: $i] : (l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))) <=> ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))), ((l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> (l1_orders_2(A) => ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))))), rewrite((l1_orders_2(A) => ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))), ((l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(99,plain,
% 0.22/0.46 (![A: $i] : (l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[98])).
% 0.22/0.46 tff(100,axiom,(![A: $i] : (l1_orders_2(A) => ![B: $i] : (l1_orders_2(B) => ![C: $i] : ((v1_orders_2(C) & l1_orders_2(C)) => ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_latsum_1')).
% 0.22/0.46 tff(101,plain,
% 0.22/0.46 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.22/0.46 tff(102,plain,
% 0.22/0.46 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.22/0.46 tff(103,plain,(
% 0.22/0.46 ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~(v1_orders_2(C) & l1_orders_2(C))) | ((C = k1_latsum_1(A, B)) <=> ((u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B))) & (u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[102])).
% 0.22/0.46 tff(104,plain,
% 0.22/0.46 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.22/0.46 tff(105,plain,
% 0.22/0.46 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.22/0.46 tff(106,plain,
% 0.22/0.46 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B)))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(107,plain,
% 0.22/0.46 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B)))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(108,plain,
% 0.22/0.46 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A), u1_orders_2(B)), k7_relset_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A, B)))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.46 tff(109,plain,
% 0.22/0.46 (![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[108, 30, 105])).
% 0.22/0.46 tff(110,plain,
% 0.22/0.46 (((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B))))))) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(111,plain,
% 0.22/0.46 ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B))))))) | ((~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(112,plain,
% 0.22/0.46 ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A!0), u1_orders_2(B)))))) <=> (C = k1_latsum_1(A!0, B))))))) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.46 tff(113,plain,
% 0.22/0.46 (![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[112, 29, 109])).
% 0.22/0.46 tff(114,plain,
% 0.22/0.46 (((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))) <=> ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(115,plain,
% 0.22/0.46 (((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))) <=> ((~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(116,plain,
% 0.22/0.47 ((~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))) <=> (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(117,plain,
% 0.22/0.47 ((((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))) <=> (((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(118,plain,
% 0.22/0.47 ((~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))) <=> (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[117])).
% 0.22/0.47 tff(119,plain,
% 0.22/0.47 ((~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))) <=> (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[118, 116])).
% 0.22/0.47 tff(120,plain,
% 0.22/0.47 (((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))) <=> ((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[119])).
% 0.22/0.47 tff(121,plain,
% 0.22/0.47 (((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))) <=> ((~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[120, 115])).
% 0.22/0.47 tff(122,plain,
% 0.22/0.47 (((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | ((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))) <=> ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[121])).
% 0.22/0.47 tff(123,plain,
% 0.22/0.47 (((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | ((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))) <=> ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[122, 114])).
% 0.22/0.47 tff(124,plain,
% 0.22/0.47 ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | ((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(125,plain,
% 0.22/0.47 ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | (~(((~(u1_struct_0(C) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (C = k1_latsum_1(A!0, B!1)))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.22/0.47 tff(126,plain,
% 0.22/0.47 ((~v1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))) | (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[125, 113, 89])).
% 0.22/0.47 tff(127,plain,
% 0.22/0.47 (~(((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[126, 86])).
% 0.22/0.47 tff(128,plain,
% 0.22/0.47 ((((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))) | (~((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1))))))) | (~(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(129,plain,
% 0.22/0.47 ((((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) <=> (g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))) = k1_latsum_1(A!0, B!1))) | (~((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[128, 83])).
% 0.22/0.47 tff(130,plain,
% 0.22/0.47 (~((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[129, 127])).
% 0.22/0.47 tff(131,plain,
% 0.22/0.47 (((~(u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (~(u1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(k2_xboole_0(u1_orders_2(A!0), u1_orders_2(B!1)), k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(B!1), u1_struct_0(B!1), u1_orders_2(A!0), u1_orders_2(B!1)))))) | (u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(132,plain,
% 0.22/0.48 (u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.22/0.48 tff(133,plain,
% 0.22/0.48 (k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = u1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(symmetry,[status(thm)],[132])).
% 0.22/0.48 tff(134,plain,
% 0.22/0.48 (k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = u1_struct_0(k1_latsum_1(A!0, B!1))),
% 0.22/0.48 inference(transitivity,[status(thm)],[133, 82])).
% 0.22/0.48 tff(135,plain,
% 0.22/0.48 (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[134])).
% 0.22/0.48 tff(136,plain,
% 0.22/0.48 (r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) <=> r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.22/0.48 inference(symmetry,[status(thm)],[135])).
% 0.22/0.48 tff(137,plain,
% 0.22/0.48 ((v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1)))) | (~v3_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(138,plain,
% 0.22/0.48 (~v3_struct_0(k1_latsum_1(A!0, B!1))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[137, 35])).
% 0.22/0.48 tff(139,plain,
% 0.22/0.48 (l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) <=> l1_struct_0(k1_latsum_1(A!0, B!1))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[83])).
% 0.22/0.48 tff(140,plain,
% 0.22/0.48 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(141,plain,
% 0.22/0.48 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.22/0.48 tff(142,plain,
% 0.22/0.48 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(143,plain,
% 0.22/0.48 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(144,plain,
% 0.22/0.48 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[143])).
% 0.22/0.48 tff(145,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.22/0.48 tff(146,plain,
% 0.22/0.48 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.22/0.48 tff(147,plain,
% 0.22/0.48 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.22/0.48 tff(148,plain,(
% 0.22/0.48 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(skolemize,[status(sab)],[147])).
% 0.22/0.48 tff(149,plain,
% 0.22/0.48 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.22/0.48 tff(150,plain,
% 0.22/0.48 (((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(151,plain,
% 0.22/0.48 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(152,plain,
% 0.22/0.48 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.22/0.48 tff(153,plain,
% 0.22/0.48 (l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))) | (~l1_orders_2(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.22/0.48 tff(154,plain,
% 0.22/0.48 (l1_struct_0(g1_orders_2(u1_struct_0(k1_latsum_1(A!0, B!1)), u1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[153, 89])).
% 0.22/0.48 tff(155,plain,
% 0.22/0.48 (l1_struct_0(k1_latsum_1(A!0, B!1))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[154, 139])).
% 0.22/0.48 tff(156,plain,
% 0.22/0.48 (^[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))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(157,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[156])).
% 0.22/0.48 tff(158,plain,
% 0.22/0.48 (^[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)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(159,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[158])).
% 0.22/0.48 tff(160,plain,
% 0.22/0.48 (![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))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(161,plain,
% 0.22/0.48 (^[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)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(162,plain,
% 0.22/0.48 (![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))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[161])).
% 0.22/0.48 tff(163,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.22/0.48 tff(164,plain,
% 0.22/0.48 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.22/0.48 tff(165,plain,
% 0.22/0.48 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.22/0.48 tff(166,plain,(
% 0.22/0.48 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[165])).
% 0.22/0.48 tff(167,plain,
% 0.22/0.48 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.22/0.48 tff(168,plain,
% 0.22/0.48 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.22/0.48 tff(169,plain,
% 0.22/0.48 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(170,plain,
% 0.22/0.48 ((v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))) | (~l1_struct_0(k1_latsum_1(A!0, B!1)))) <=> (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(171,plain,
% 0.22/0.48 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))) | (~l1_struct_0(k1_latsum_1(A!0, B!1))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[170])).
% 0.22/0.48 tff(172,plain,
% 0.22/0.48 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))) | (~l1_struct_0(k1_latsum_1(A!0, B!1))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[171, 169])).
% 0.22/0.48 tff(173,plain,
% 0.22/0.48 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))) | (~l1_struct_0(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(174,plain,
% 0.22/0.48 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.22/0.48 tff(175,plain,
% 0.22/0.48 (v3_struct_0(k1_latsum_1(A!0, B!1)) | (~l1_struct_0(k1_latsum_1(A!0, B!1))) | (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[174, 168])).
% 0.22/0.48 tff(176,plain,
% 0.22/0.48 (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[175, 155, 138])).
% 0.22/0.48 tff(177,plain,
% 0.22/0.48 (^[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))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(178,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[177])).
% 0.22/0.48 tff(179,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(180,plain,
% 0.22/0.48 (^[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))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(181,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[180])).
% 0.22/0.48 tff(182,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.22/0.48 tff(183,plain,
% 0.22/0.48 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.22/0.48 tff(184,plain,
% 0.22/0.48 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.22/0.48 tff(185,plain,(
% 0.22/0.48 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.22/0.48 inference(skolemize,[status(sab)],[184])).
% 0.22/0.48 tff(186,plain,
% 0.22/0.48 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.22/0.48 tff(187,plain,
% 0.22/0.48 (~(r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | r2_hidden(C!2, u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(and_elim,[status(thm)],[28])).
% 0.22/0.48 tff(188,plain,
% 0.22/0.48 (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(or_elim,[status(thm)],[187])).
% 0.22/0.48 tff(189,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(190,plain,
% 0.22/0.48 ((r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))) <=> ((~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(191,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[190])).
% 0.22/0.48 tff(192,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[191, 189])).
% 0.22/0.48 tff(193,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(194,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))) | v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.22/0.48 tff(195,plain,
% 0.22/0.48 (v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1))) | r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[194, 188, 186])).
% 0.22/0.48 tff(196,plain,
% 0.22/0.48 (r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[195, 176])).
% 0.22/0.48 tff(197,plain,
% 0.22/0.48 (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[196, 136])).
% 0.22/0.48 tff(198,plain,
% 0.22/0.48 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(199,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[198])).
% 0.22/0.48 tff(200,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(pull_quant,[status(thm)],[])).
% 0.22/0.48 tff(201,plain,
% 0.22/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) <=> ![D: $i] : ((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))), ((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) <=> (~![D: $i] : ((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))))), pull_quant((~![D: $i] : ((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) <=> ?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))))), ((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) <=> ?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))))), (((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))), (((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))), ((~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))), ((~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(202,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[201])).
% 0.22/0.48 tff(203,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[202, 200])).
% 0.22/0.48 tff(204,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[203, 199])).
% 0.22/0.48 tff(205,plain,
% 0.22/0.48 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(206,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[205])).
% 0.22/0.48 tff(207,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[206, 204])).
% 0.22/0.48 tff(208,plain,
% 0.22/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) <=> ((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))), trans(monotonicity(trans(monotonicity(rewrite((r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))) <=> (r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))), ((~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))) <=> (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))), rewrite((~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))) <=> (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))), ((~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))) <=> (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))), (((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))) <=> ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))), rewrite(((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))) <=> ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))), (((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))) <=> ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))), ((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))) <=> (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))))), rewrite((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))), ((((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))) <=> (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(209,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[208])).
% 0.22/0.48 tff(210,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(211,axiom,(![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.22/0.48 tff(212,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : ((C = k2_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.22/0.48 tff(213,plain,(
% 0.22/0.48 ![A: $i, B: $i, C: $i] : (((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B)))) & ((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[212])).
% 0.22/0.48 tff(214,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = k2_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.22/0.48 tff(215,plain,
% 0.22/0.48 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.22/0.48 tff(216,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k2_xboole_0(A, B))) | (r2_hidden(D, C) <=> (r2_hidden(D, A) | r2_hidden(D, B))))) | (~((C = k2_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_3(C, B, A), C) <=> (r2_hidden(tptp_fun_D_3(C, B, A), A) | r2_hidden(tptp_fun_D_3(C, B, A), B))))))))) | (~((~((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~((k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~(r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(217,plain,
% 0.22/0.48 (~((~((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~((k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~(r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.22/0.48 tff(218,plain,
% 0.22/0.48 (((~((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~((k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~(r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | r2_hidden(tptp_fun_D_3(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(A!0)), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))) | ((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(219,plain,
% 0.22/0.48 ((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.22/0.48 tff(220,plain,
% 0.22/0.48 (^[A: $i, B: $i] : refl((k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)) <=> (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(221,plain,
% 0.22/0.49 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[220])).
% 0.22/0.49 tff(222,plain,
% 0.22/0.49 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B)) <=> ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(223,axiom,(![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t39_xboole_1')).
% 0.22/0.49 tff(224,plain,
% 0.22/0.49 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.22/0.49 tff(225,plain,(
% 0.22/0.49 ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.22/0.49 inference(skolemize,[status(sab)],[224])).
% 0.22/0.49 tff(226,plain,
% 0.22/0.49 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.22/0.49 tff(227,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))) | (k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(228,plain,
% 0.22/0.49 (k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) = k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.22/0.49 tff(229,plain,
% 0.22/0.49 (k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.22/0.49 inference(symmetry,[status(thm)],[228])).
% 0.22/0.49 tff(230,plain,
% 0.22/0.49 ((~((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(231,plain,
% 0.22/0.49 ((~((~(k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k2_xboole_0(u1_struct_0(A!0), k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.22/0.49 tff(232,plain,
% 0.22/0.49 (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[231, 219])).
% 0.22/0.49 tff(233,plain,
% 0.22/0.49 (~r2_hidden(C!2, u1_struct_0(A!0))),
% 0.22/0.49 inference(or_elim,[status(thm)],[187])).
% 0.22/0.49 tff(234,plain,
% 0.22/0.49 (~r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.22/0.49 inference(or_elim,[status(thm)],[187])).
% 0.22/0.49 tff(235,plain,
% 0.22/0.49 ((~(r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(236,plain,
% 0.22/0.49 (~(r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[235, 234, 233])).
% 0.22/0.49 tff(237,plain,
% 0.22/0.49 ((~(r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(238,plain,
% 0.22/0.49 ((~(r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.22/0.49 tff(239,plain,
% 0.22/0.49 (~r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[238, 232])).
% 0.22/0.49 tff(240,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[239, 197])).
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------