TSTP Solution File: SEU407+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU407+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Tue Sep 20 07:29:22 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU407+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 13:24:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(r2_hidden_type, type, (
% 0.19/0.42 r2_hidden: ( $i * $i ) > $o)).
% 0.19/0.42 tff(k2_xboole_0_type, type, (
% 0.19/0.42 k2_xboole_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(u1_struct_0_type, type, (
% 0.19/0.42 u1_struct_0: $i > $i)).
% 0.19/0.42 tff(tptp_fun_B_1_type, type, (
% 0.19/0.42 tptp_fun_B_1: $i)).
% 0.19/0.42 tff(tptp_fun_A_0_type, type, (
% 0.19/0.42 tptp_fun_A_0: $i)).
% 0.19/0.42 tff(tptp_fun_C_2_type, type, (
% 0.19/0.42 tptp_fun_C_2: $i)).
% 0.19/0.42 tff(k1_latsum_1_type, type, (
% 0.19/0.42 k1_latsum_1: ( $i * $i ) > $i)).
% 0.19/0.42 tff(g1_orders_2_type, type, (
% 0.19/0.42 g1_orders_2: ( $i * $i ) > $i)).
% 0.19/0.42 tff(u1_orders_2_type, type, (
% 0.19/0.42 u1_orders_2: $i > $i)).
% 0.19/0.42 tff(v1_orders_2_type, type, (
% 0.19/0.42 v1_orders_2: $i > $o)).
% 0.19/0.42 tff(v3_struct_0_type, type, (
% 0.19/0.42 v3_struct_0: $i > $o)).
% 0.19/0.42 tff(l1_orders_2_type, type, (
% 0.19/0.42 l1_orders_2: $i > $o)).
% 0.19/0.42 tff(m1_subset_1_type, type, (
% 0.19/0.42 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.42 tff(k4_xboole_0_type, type, (
% 0.19/0.42 k4_xboole_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(k7_relset_1_type, type, (
% 0.19/0.42 k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.42 tff(v1_xboole_0_type, type, (
% 0.19/0.42 v1_xboole_0: $i > $o)).
% 0.19/0.42 tff(l1_struct_0_type, type, (
% 0.19/0.42 l1_struct_0: $i > $o)).
% 0.19/0.42 tff(tptp_fun_D_3_type, type, (
% 0.19/0.42 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (^[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)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (^[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))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.42 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/sandbox2/benchmark/theBenchmark.p','fc2_latsum_1')).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.42 tff(11,plain,(
% 0.19/0.42 ![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))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[10])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 ((((~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)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 ((((~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)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 ((~(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))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 ((~(~((~v3_struct_0(B!1)) & l1_orders_2(B!1)))) <=> ((~v3_struct_0(B!1)) & l1_orders_2(B!1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (((~(~((~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)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[17, 16])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (((~(~((~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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[18, 15])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 ((~(~((~v3_struct_0(A!0)) & l1_orders_2(A!0)))) <=> ((~v3_struct_0(A!0)) & l1_orders_2(A!0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (((~(~((~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))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[20, 19])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (((~(~((~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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[21, 14])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 ((~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 ((~![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (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))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(25,axiom,(~![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (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/sandbox2/benchmark/theBenchmark.p','t7_latsum_1')).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : (r2_hidden(C, 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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 ((~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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (l1_orders_2(B!1)),
% 0.19/0.43 inference(and_elim,[status(thm)],[33])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (l1_orders_2(A!0)),
% 0.19/0.43 inference(and_elim,[status(thm)],[33])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (~v3_struct_0(A!0)),
% 0.19/0.43 inference(and_elim,[status(thm)],[33])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (((~![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))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 ((~![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))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((~![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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (~(v3_struct_0(k1_latsum_1(A!0, B!1)) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[39, 36, 35, 34, 13])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 ((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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (v1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.43 tff(50,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/sandbox2/benchmark/theBenchmark.p','dt_k1_latsum_1')).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.43 tff(53,plain,(
% 0.19/0.43 ![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))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[52])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (((~![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))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (((~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))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 ((~((~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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (((~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))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (((~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))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (((~![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)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (((~![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))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[61, 56])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 ((~![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))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 ((~![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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (~((~l1_orders_2(k1_latsum_1(A!0, B!1))) | (~v1_orders_2(k1_latsum_1(A!0, B!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[64, 35, 34, 55])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (((~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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (l1_orders_2(k1_latsum_1(A!0, B!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.43 tff(73,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/sandbox2/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.43 tff(76,plain,(
% 0.19/0.43 ![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[75])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (![A: $i] : ((A = g1_orders_2(u1_struct_0(A), u1_orders_2(A))) | (~v1_orders_2(A)) | (~l1_orders_2(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (((~![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (((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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (((~![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)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (((~![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))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 ((~![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))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 ((~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)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[83, 77])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[84, 67, 42])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (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))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(symmetry,[status(thm)],[86])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(symmetry,[status(thm)],[85])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (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))))),
% 0.19/0.44 inference(symmetry,[status(thm)],[89])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[42, 90])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (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))))),
% 0.19/0.44 inference(symmetry,[status(thm)],[92])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[67, 93])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (^[A: $i] : refl(((~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))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (^[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)) | ((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))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (^[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)) | ((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))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (![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)))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (^[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)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (![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)))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.44 tff(105,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/sandbox2/benchmark/theBenchmark.p','d2_latsum_1')).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![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)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (![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)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.19/0.44 tff(108,plain,(
% 0.19/0.44 ![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)))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[107])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (((~![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)))))))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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)))))))))))) <=> ((~![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)))))))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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)))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 ((~![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)))))))))))) | ((~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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)))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 ((~![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)))))))))))) | (~l1_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 (![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[113, 35, 110])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 (((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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))))))))))) | ((~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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))))))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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))))))))))) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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))))))))))) | ((~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 ((~![B: $i] : ((~l1_orders_2(B)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B)) <=> (~((~(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))))))))))) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[117, 34, 114])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | ((~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))))) | ((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)))))))))) <=> ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | (~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))))) | ((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)))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (((~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))))) | (~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))))) | ((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))))))))) <=> ((~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))))) | ((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)))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 ((~((~(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)))) = 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)))) | (~(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)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (((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)) <=> (~((~(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))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (((~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))))) | (~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))))) | ((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))))))))) <=> ((~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))))) | ((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)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (((~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))))) | (~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))))) | ((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))))))))) <=> ((~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))))) | ((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)))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[123, 120])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | ((~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))))) | ((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)))))))))) <=> ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | ((~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))))) | ((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))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | ((~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))))) | ((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)))))))))) <=> ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | (~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))))) | ((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)))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[125, 119])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | ((~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))))) | ((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)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 ((~![C: $i] : ((~v1_orders_2(C)) | (~l1_orders_2(C)) | ((C = k1_latsum_1(A!0, B!1)) <=> (~((~(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)))))))))) | (~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))))) | ((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))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 ((~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))))) | ((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))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[128, 118, 94])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 ((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)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[129, 91])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 ((~((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))) | (~((~(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)))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~((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))))))))) | (~((~(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)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[131, 88])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (~((~(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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[132, 130])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (((~(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)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (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))))),
% 0.19/0.46 inference(symmetry,[status(thm)],[135])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = u1_struct_0(k1_latsum_1(A!0, B!1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[136, 87])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 (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)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (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)))),
% 0.19/0.46 inference(symmetry,[status(thm)],[138])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 ((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)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (~v3_struct_0(k1_latsum_1(A!0, B!1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[140, 40])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (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))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.46 tff(148,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.19/0.46 tff(151,plain,(
% 0.19/0.46 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[150])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 (((~![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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 ((~![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))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 ((~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (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))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[156, 94])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (l1_struct_0(k1_latsum_1(A!0, B!1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[157, 142])).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[161])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.46 tff(166,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.19/0.46 tff(169,plain,(
% 0.19/0.46 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[168])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[170, 160])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 (((~![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)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 ((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)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 (((~![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))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[173])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(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)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[174, 172])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 (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))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[177, 171])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (~v1_xboole_0(u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[178, 158, 141])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[183])).
% 0.19/0.47 tff(185,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.19/0.47 tff(188,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[187])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 (~(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)))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[33])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 (m1_subset_1(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.19/0.47 inference(or_elim,[status(thm)],[190])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 ((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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (((~![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)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[193])).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[194, 192])).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 ((~![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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[197, 191, 189])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (r2_hidden(C!2, u1_struct_0(k1_latsum_1(A!0, B!1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[198, 179])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[199, 139])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 (^[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))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[201])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(pull_quant,[status(thm)],[])).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[204])).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[205, 203])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[206, 202])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 (^[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))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[208])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[209, 207])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (^[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))))), 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)))), (((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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[213])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(216,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/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.47 tff(218,plain,(
% 0.19/0.47 ![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))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[217])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[220, 210])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 ((~![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)))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 (~((~((~(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))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 (((~((~(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))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(225,plain,
% 0.19/0.47 ((~(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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 (^[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)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.47 tff(228,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(229,axiom,(![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t39_xboole_1')).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.47 tff(231,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.19/0.47 inference(skolemize,[status(sab)],[230])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (![A: $i, B: $i] : (k2_xboole_0(A, k4_xboole_0(B, A)) = k2_xboole_0(A, B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (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)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[234])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 ((~((~(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(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)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 ((~((~(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))))))) | (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)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(A!0)) | r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[237, 225])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 (~r2_hidden(C!2, u1_struct_0(A!0))),
% 0.19/0.48 inference(or_elim,[status(thm)],[190])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 (~r2_hidden(C!2, k4_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.19/0.48 inference(or_elim,[status(thm)],[190])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 ((~(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)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (~(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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[241, 240, 239])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 ((~(r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(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))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 ((~(r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> (r2_hidden(C!2, u1_struct_0(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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 (~r2_hidden(C!2, k2_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[244, 238])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[245, 200])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------