TSTP Solution File: SEU411+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU411+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 07:29:25 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU411+1 : TPTP v8.1.0. Released v3.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 13:34:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(v1_xboole_0_type, type, (
% 0.20/0.47 v1_xboole_0: $i > $o)).
% 0.20/0.47 tff(k1_xboole_0_type, type, (
% 0.20/0.47 k1_xboole_0: $i)).
% 0.20/0.47 tff(k3_xboole_0_type, type, (
% 0.20/0.47 k3_xboole_0: ( $i * $i ) > $i)).
% 0.20/0.47 tff(u1_struct_0_type, type, (
% 0.20/0.47 u1_struct_0: $i > $i)).
% 0.20/0.47 tff(tptp_fun_B_1_type, type, (
% 0.20/0.47 tptp_fun_B_1: $i)).
% 0.20/0.47 tff(tptp_fun_A_0_type, type, (
% 0.20/0.47 tptp_fun_A_0: $i)).
% 0.20/0.47 tff(r2_hidden_type, type, (
% 0.20/0.47 r2_hidden: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_B_4_type, type, (
% 0.20/0.47 tptp_fun_B_4: $i > $i)).
% 0.20/0.47 tff(r1_orders_2_type, type, (
% 0.20/0.47 r1_orders_2: ( $i * $i * $i ) > $o)).
% 0.20/0.47 tff(k3_yellow_0_type, type, (
% 0.20/0.47 k3_yellow_0: $i > $i)).
% 0.20/0.47 tff(m1_subset_1_type, type, (
% 0.20/0.47 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_D_5_type, type, (
% 0.20/0.47 tptp_fun_D_5: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(v1_yellow_0_type, type, (
% 0.20/0.47 v1_yellow_0: $i > $o)).
% 0.20/0.47 tff(v4_orders_2_type, type, (
% 0.20/0.47 v4_orders_2: $i > $o)).
% 0.20/0.47 tff(l1_orders_2_type, type, (
% 0.20/0.47 l1_orders_2: $i > $o)).
% 0.20/0.47 tff(v3_struct_0_type, type, (
% 0.20/0.47 v3_struct_0: $i > $o)).
% 0.20/0.47 tff(v1_lattice3_type, type, (
% 0.20/0.47 v1_lattice3: $i > $o)).
% 0.20/0.47 tff(v3_orders_2_type, type, (
% 0.20/0.47 v3_orders_2: $i > $o)).
% 0.20/0.47 tff(v2_orders_2_type, type, (
% 0.20/0.47 v2_orders_2: $i > $o)).
% 0.20/0.47 tff(k1_zfmisc_1_type, type, (
% 0.20/0.47 k1_zfmisc_1: $i > $i)).
% 0.20/0.47 tff(v12_waybel_0_type, type, (
% 0.20/0.47 v12_waybel_0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(v1_waybel_0_type, type, (
% 0.20/0.47 v1_waybel_0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_C_2_type, type, (
% 0.20/0.47 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.47 tff(tptp_fun_D_3_type, type, (
% 0.20/0.47 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.20/0.47 tff(l1_struct_0_type, type, (
% 0.20/0.47 l1_struct_0: $i > $o)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(4,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.47 tff(6,plain,(
% 0.20/0.47 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.20/0.47 inference(skolemize,[status(sab)],[5])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.20/0.47 inference(symmetry,[status(thm)],[9])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(pull_quant,[status(thm)],[])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B)))))) <=> ![D: $i] : ((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))), ((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) <=> (~![D: $i] : ((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))))), pull_quant((~![D: $i] : ((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) <=> ?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B)))))))), ((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) <=> ?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))))), (((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))), (((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))), ((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))), ((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[16, 12])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) <=> ((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))), rewrite(((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B)))) <=> ((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))), ((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B))))) <=> (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B)))))) & ((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))))), rewrite((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B)))))) & ((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B)))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))), ((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_5(C, B, A), C) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B)))))) <=> (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_5(C, B, A), C) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((C = k3_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 = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(26,axiom,(![A: $i, B: $i, C: $i] : ((C = k3_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','d3_xboole_0')).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.47 tff(28,plain,(
% 0.20/0.47 ![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_5(C, B, A), C) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[27])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_5(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_5(C, B, A), A) & r2_hidden(tptp_fun_D_5(C, B, A), B)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 ((~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))))) <=> (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (~((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 31])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))) | (r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> ((~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_D_5(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), u1_struct_0(B!1), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))))) | ((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 ((~(~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (($false | (~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> (~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 ((~$true) <=> $false),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | $true) <=> $true),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) <=> $true),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ((~(~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 ((~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> (~(~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 ((r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))) <=> (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 ((r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))) <=> $true),
% 0.20/0.48 inference(transitivity,[status(thm)],[52, 47])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | $true)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> $true),
% 0.20/0.48 inference(transitivity,[status(thm)],[54, 46])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 ((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) <=> (~$true)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 ((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) <=> $false),
% 0.20/0.48 inference(transitivity,[status(thm)],[56, 45])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))))) <=> ($false | (~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[57, 44])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))))) <=> (~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[58, 43])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 ((~((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))))) <=> (~(~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 ((~((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))))) <=> (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[60, 42])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[62, 41])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (~((~((~(u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)) <=> (~((~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(u1_struct_0(A!0)), u1_struct_0(A!0)))))))) | (~((u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> ((~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_D_5(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, A)) | (~r2_hidden(D, B))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_5(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_5(C, B, A), A)) | (~r2_hidden(tptp_fun_D_5(C, B, A), B))))))))) | (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (u1_struct_0(A!0) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[65, 31])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)) = u1_struct_0(A!0)),
% 0.20/0.49 inference(symmetry,[status(thm)],[66])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))),
% 0.20/0.49 inference(symmetry,[status(thm)],[68])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[10, 69])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 ((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))) | (~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 ((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k3_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(B!1)))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))))) | (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[72, 40])).
% 0.20/0.49 tff(74,assumption,(r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))), introduced(assumption)).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 ((~(r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 ((~(r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) <=> (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))))) | (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (~((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.49 tff(85,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.49 tff(88,plain,(
% 0.20/0.49 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(skolemize,[status(sab)],[87])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[99, 97])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))), ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))), ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))))), (((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ((v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))), (((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) <=> ((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A))), (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> (((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A)) & l1_orders_2(A)))), rewrite((((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))), (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))), ((((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B))) <=> (((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))))), rewrite((((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B))) <=> ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))), ((((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B))) <=> ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (![A: $i] : (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.49 tff(106,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_orders_2(A, k3_yellow_0(A), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_yellow_0')).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.49 tff(109,plain,(
% 0.20/0.49 ![A: $i] : ((~((~v3_struct_0(A)) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[108])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[111, 95])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))) <=> ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ((~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))) <=> (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 ((~(~((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)))) <=> ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (((~(~((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)))) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))) <=> (((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[115, 114])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (((~(~((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0)))) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))) <=> ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[116, 113])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 ((~![A: $i] : ((((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & v1_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_yellow_0(B)) & v1_lattice3(B)) & l1_orders_2(B)) => (((((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) => r2_hidden(k3_yellow_0(B), u1_struct_0(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(120,axiom,(~![A: $i] : ((((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & v1_yellow_0(A)) & v1_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_yellow_0(B)) & v1_lattice3(B)) & l1_orders_2(B)) => (((((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B)) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B)))) => r2_hidden(k3_yellow_0(B), u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_latsum_1')).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[123, 118])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[124, 118])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A))) | ![B: $i] : (r2_hidden(k3_yellow_0(B), u1_struct_0(A)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), B) & m1_subset_1(k3_xboole_0(u1_struct_0(A), u1_struct_0(B)), k1_zfmisc_1(u1_struct_0(B))))) | (~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[126, 118])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 ((~v3_struct_0(A!0)) & v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_yellow_0(A!0) & v1_lattice3(A!0) & l1_orders_2(A!0) & (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (~(r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | (~((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))))) | (~((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1))))),
% 0.20/0.50 inference(and_elim,[status(thm)],[128])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 ((~v3_struct_0(B!1)) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_yellow_0(B!1) & v1_lattice3(B!1) & l1_orders_2(B!1)),
% 0.20/0.50 inference(or_elim,[status(thm)],[129])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (l1_orders_2(B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[130])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (v1_yellow_0(B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[130])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 (v4_orders_2(B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[130])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (~v3_struct_0(B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[130])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v4_orders_2(A)) | (~v1_yellow_0(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_orders_2(A, k3_yellow_0(A), B)))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_yellow_0(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[137, 134, 133, 132, 131, 112])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), B))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[141, 138, 93])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 (v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) <=> v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) <=> v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)),
% 0.20/0.50 inference(symmetry,[status(thm)],[143])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 ((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1) & m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.50 inference(or_elim,[status(thm)],[129])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (v12_waybel_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[145])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[146, 144])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[148])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (m1_subset_1(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.50 inference(and_elim,[status(thm)],[145])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[152])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 (^[A: $i] : refl(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[157, 155])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 (^[A: $i] : rewrite(((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | ((~(~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)))) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | ((~(~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)))) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A)))))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))) <=> (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))), ((l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))))) <=> (l1_orders_2(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))))), rewrite((l1_orders_2(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))), ((l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))))) <=> ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (![A: $i] : (l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.50 tff(166,axiom,(![A: $i] : (l1_orders_2(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v12_waybel_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r1_orders_2(A, D, C)) => r2_hidden(D, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d19_waybel_0')).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v12_waybel_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.20/0.50 tff(169,plain,(
% 0.20/0.50 ![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | ((~(~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)))) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))))))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[168])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~(r2_hidden(C, B) & r1_orders_2(A, D, C))) | (~m1_subset_1(D, u1_struct_0(A)))))) & (v12_waybel_0(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~(r2_hidden(tptp_fun_D_3(B, A), B) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[170, 160])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C)))))) | (~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A)))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[171, 158])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[172, 153])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 (((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C)))))))))) <=> ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 (((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | ((~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_hidden(C, B)) | (~r1_orders_2(B!1, D, C))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 ((~![A: $i] : ((~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v12_waybel_0(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | r2_hidden(tptp_fun_D_3(B, A), B) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r1_orders_2(A, tptp_fun_D_3(B, A), tptp_fun_C_2(B, A))))))) | (~((~v12_waybel_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(D, B) | (~m1_subset_1(D, u1_struct_0(A))) | (~r2_hidden(C, B)) | (~r1_orders_2(A, D, C))))))))))) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[179, 131, 173])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 (((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C))))))))) <=> ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_2(B, B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(B, B!1), B) | (~m1_subset_1(tptp_fun_D_3(B, B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(B, B!1), B)) | (~r1_orders_2(B!1, tptp_fun_D_3(B, B!1), tptp_fun_C_2(B, B!1))))))) | (~((~v12_waybel_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : (r2_hidden(D, B) | (~r2_hidden(C, B)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)))))))))) | (~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.52 tff(187,plain,
% 0.20/0.52 ((~m1_subset_1(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[186, 180])).
% 0.20/0.52 tff(188,plain,
% 0.20/0.52 (~((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[187, 151])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 (((~(v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1) | (~((~m1_subset_1(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | r2_hidden(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), u1_struct_0(B!1))) | (~r2_hidden(tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, tptp_fun_D_3(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1), tptp_fun_C_2(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1))))))) | (~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))) | ((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(190,plain,
% 0.20/0.52 ((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 ((~((~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))) | (~v12_waybel_0(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)), B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[191, 190, 147])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 (((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) <=> ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[195, 193])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~r1_orders_2(B!1, D, C)) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 ((~m1_subset_1(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[198, 192])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[199, 93])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[201])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[203])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[204, 202])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A))))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & l1_orders_2(B)) <=> (~(v3_struct_0(B) | (~l1_orders_2(B))))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (~(~(v3_struct_0(B) | (~l1_orders_2(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_orders_2(B))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (v3_struct_0(B) | (~l1_orders_2(B))))), (((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), rewrite(((v3_struct_0(B) | (~l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), (((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), (![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))) <=> ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), (![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))) <=> ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), ((((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))) <=> (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), rewrite((((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))) <=> ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))), ((((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))) <=> ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), (![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))))) <=> (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[209])).
% 0.20/0.53 tff(211,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(B)) & l1_orders_2(B)) => ![C: $i] : (r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(C, u1_struct_0(B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_latsum_1')).
% 0.20/0.53 tff(212,plain,
% 0.20/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.53 tff(213,plain,
% 0.20/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.20/0.53 tff(214,plain,(
% 0.20/0.53 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[213])).
% 0.20/0.53 tff(215,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.20/0.53 tff(216,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[215, 205])).
% 0.20/0.53 tff(217,plain,
% 0.20/0.53 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(218,plain,
% 0.20/0.53 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(219,plain,
% 0.20/0.53 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.53 tff(220,plain,
% 0.20/0.53 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[219, 134, 131, 216])).
% 0.20/0.53 tff(221,plain,
% 0.20/0.53 (l1_orders_2(A!0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[128])).
% 0.20/0.53 tff(222,plain,
% 0.20/0.53 (~v3_struct_0(A!0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[128])).
% 0.20/0.53 tff(223,plain,
% 0.20/0.53 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(224,plain,
% 0.20/0.53 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(225,plain,
% 0.20/0.53 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(B)))) | m1_subset_1(C, u1_struct_0(B))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.53 tff(226,plain,
% 0.20/0.53 (![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[225, 222, 221, 220])).
% 0.20/0.53 tff(227,plain,
% 0.20/0.53 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(228,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[227])).
% 0.20/0.53 tff(229,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(230,plain,
% 0.20/0.53 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(231,plain,
% 0.20/0.53 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[230])).
% 0.20/0.53 tff(232,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.20/0.53 tff(233,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.53 tff(234,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.20/0.53 tff(235,plain,(
% 0.20/0.53 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[234])).
% 0.20/0.53 tff(236,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.20/0.53 tff(237,plain,
% 0.20/0.53 (((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(238,plain,
% 0.20/0.53 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(239,plain,
% 0.20/0.53 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.53 tff(240,plain,
% 0.20/0.53 (l1_struct_0(A!0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[239, 221, 236])).
% 0.20/0.53 tff(241,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[241])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 (^[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)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[243])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 (^[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)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[246])).
% 0.20/0.53 tff(248,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')).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.20/0.53 tff(251,plain,(
% 0.20/0.53 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[250])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[252, 242])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[259, 222, 253, 240])).
% 0.20/0.53 tff(261,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(262,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[261])).
% 0.20/0.53 tff(263,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(264,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(265,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[264])).
% 0.20/0.53 tff(266,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')).
% 0.20/0.53 tff(267,plain,
% 0.20/0.53 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.53 tff(268,plain,
% 0.20/0.53 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.20/0.53 tff(269,plain,(
% 0.20/0.53 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[268])).
% 0.20/0.53 tff(270,plain,
% 0.20/0.53 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.20/0.53 tff(271,plain,
% 0.20/0.53 (~r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0))),
% 0.20/0.53 inference(or_elim,[status(thm)],[129])).
% 0.20/0.53 tff(272,plain,
% 0.20/0.53 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(273,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(274,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | r2_hidden(k3_yellow_0(B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.53 tff(275,plain,
% 0.20/0.53 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[274, 271, 270])).
% 0.20/0.53 tff(276,plain,
% 0.20/0.53 (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[275, 260])).
% 0.20/0.53 tff(277,plain,
% 0.20/0.53 (((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(278,plain,
% 0.20/0.53 ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(279,plain,
% 0.20/0.53 ((~![C: $i] : ((~r2_hidden(C, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(A!0))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.53 tff(280,plain,
% 0.20/0.53 (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[279, 276, 226])).
% 0.20/0.53 tff(281,plain,
% 0.20/0.53 (^[A: $i] : refl(((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(282,plain,
% 0.20/0.53 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[281])).
% 0.20/0.53 tff(283,plain,
% 0.20/0.53 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(284,plain,
% 0.20/0.53 (^[A: $i] : rewrite((l1_orders_2(A) => m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(285,plain,
% 0.20/0.53 (![A: $i] : (l1_orders_2(A) => m1_subset_1(k3_yellow_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[284])).
% 0.20/0.53 tff(286,axiom,(![A: $i] : (l1_orders_2(A) => m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_yellow_0')).
% 0.20/0.53 tff(287,plain,
% 0.20/0.53 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.53 tff(288,plain,
% 0.20/0.53 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.20/0.53 tff(289,plain,(
% 0.20/0.53 ![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[288])).
% 0.20/0.53 tff(290,plain,
% 0.20/0.53 (![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[289, 282])).
% 0.20/0.53 tff(291,plain,
% 0.20/0.53 (((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | ((~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1)))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | (~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(292,plain,
% 0.20/0.53 ((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | ((~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(293,plain,
% 0.20/0.53 ((~![A: $i] : ((~l1_orders_2(A)) | m1_subset_1(k3_yellow_0(A), u1_struct_0(A)))) | (~l1_orders_2(B!1)) | m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.53 tff(294,plain,
% 0.20/0.53 (m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[293, 131, 290])).
% 0.20/0.53 tff(295,plain,
% 0.20/0.53 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | ((~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(297,plain,
% 0.20/0.53 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | r2_hidden(D, k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, D, tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))) | (~m1_subset_1(k3_yellow_0(B!1), u1_struct_0(B!1))) | r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~r1_orders_2(B!1, k3_yellow_0(B!1), tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[297, 294, 280, 74, 200, 142])).
% 0.20/0.53 tff(299,plain,(~r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 (^[A: $i, B: $i] : refl((~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(301,plain,
% 0.20/0.53 (![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[300])).
% 0.20/0.53 tff(302,plain,
% 0.20/0.53 (![A: $i] : ![B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(pull_quant,[status(thm)],[])).
% 0.20/0.53 tff(303,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) <=> ![B: $i] : ((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))), ((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) <=> (~![B: $i] : ((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))), pull_quant((~![B: $i] : ((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) <=> ?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A))))), ((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) <=> ?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))))), (((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))) <=> (?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))), pull_quant((?[B: $i] : (~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))) <=> ?[B: $i] : ((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))), (((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))) <=> ?[B: $i] : ((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))), ((~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> (~?[B: $i] : ((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))), ((~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(304,plain,
% 0.20/0.53 (![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[303])).
% 0.20/0.53 tff(305,plain,
% 0.20/0.53 (![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[304, 302])).
% 0.20/0.53 tff(306,plain,
% 0.20/0.53 (![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[305, 301])).
% 0.20/0.53 tff(307,plain,
% 0.20/0.53 (^[A: $i] : rewrite((~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(308,plain,
% 0.20/0.53 (![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[307])).
% 0.20/0.53 tff(309,plain,
% 0.20/0.53 (![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[308, 306])).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(rewrite(((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) <=> ((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))), ((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))), rewrite((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))), ((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(311,plain,
% 0.20/0.53 (![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))) <=> ![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[310])).
% 0.20/0.53 tff(312,plain,
% 0.20/0.53 (^[A: $i] : rewrite((((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | (~(~r2_hidden(tptp_fun_B_4(A), A))))) <=> (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(313,plain,
% 0.20/0.54 (![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | (~(~r2_hidden(tptp_fun_B_4(A), A))))) <=> ![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[312])).
% 0.20/0.54 tff(314,plain,
% 0.20/0.54 (![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A))) <=> ![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(315,axiom,(![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_xboole_0')).
% 0.20/0.54 tff(316,plain,
% 0.20/0.54 (![A: $i] : ((A = k1_xboole_0) <=> ![B: $i] : (~r2_hidden(B, A)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.54 tff(317,plain,(
% 0.20/0.54 ![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | (~(~r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[316])).
% 0.20/0.54 tff(318,plain,
% 0.20/0.54 (![A: $i] : (((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A))) & ((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.20/0.54 tff(319,plain,
% 0.20/0.54 (![A: $i] : (~((~((~(A = k1_xboole_0)) | ![B: $i] : (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[318, 311])).
% 0.20/0.54 tff(320,plain,
% 0.20/0.54 (![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[319, 309])).
% 0.20/0.54 tff(321,plain,
% 0.20/0.54 ((~![A: $i, B: $i] : (~((~((~(A = k1_xboole_0)) | (~r2_hidden(B, A)))) | (~((A = k1_xboole_0) | r2_hidden(tptp_fun_B_4(A), A)))))) | (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0)) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(322,plain,
% 0.20/0.54 (~((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0)) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.20/0.54 tff(323,plain,
% 0.20/0.54 (((~((~(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0)) | (~r2_hidden(k3_yellow_0(B!1), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | (~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))))) | ((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(324,plain,
% 0.20/0.54 ((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.20/0.54 tff(325,plain,
% 0.20/0.54 ((~((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))))) | (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(326,plain,
% 0.20/0.54 ((k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0) | r2_hidden(tptp_fun_B_4(k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))), k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.20/0.54 tff(327,plain,
% 0.20/0.54 (k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0)) = k1_xboole_0),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[326, 299])).
% 0.20/0.54 tff(328,plain,
% 0.20/0.54 (k1_xboole_0 = k3_xboole_0(u1_struct_0(B!1), u1_struct_0(A!0))),
% 0.20/0.54 inference(symmetry,[status(thm)],[327])).
% 0.20/0.54 tff(329,plain,
% 0.20/0.54 (k1_xboole_0 = k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.20/0.54 inference(transitivity,[status(thm)],[328, 10])).
% 0.20/0.54 tff(330,plain,
% 0.20/0.54 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[329])).
% 0.20/0.54 tff(331,plain,
% 0.20/0.54 (v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1))) <=> v1_xboole_0(k1_xboole_0)),
% 0.20/0.54 inference(symmetry,[status(thm)],[330])).
% 0.20/0.54 tff(332,plain,
% 0.20/0.54 ((~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))) <=> (~v1_xboole_0(k1_xboole_0))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[331])).
% 0.20/0.54 tff(333,plain,
% 0.20/0.54 (~v1_xboole_0(k3_xboole_0(u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[145])).
% 0.20/0.54 tff(334,plain,
% 0.20/0.54 (~v1_xboole_0(k1_xboole_0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.20/0.54 tff(335,plain,
% 0.20/0.54 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(336,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.20/0.54 tff(337,plain,
% 0.20/0.54 (v1_xboole_0(k1_xboole_0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.54 tff(338,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[337, 334])).
% 0.20/0.54 % SZS output end Proof
%------------------------------------------------------------------------------