TSTP Solution File: LAT347+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT347+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 : Sat Sep 17 18:33:19 EDT 2022
% Result : Theorem 1.33s 1.10s
% Output : Proof 1.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT347+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 15:27:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.33/1.10 % SZS status Theorem
% 1.33/1.10 % SZS output start Proof
% 1.33/1.10 tff(m1_subset_1_type, type, (
% 1.33/1.10 m1_subset_1: ( $i * $i ) > $o)).
% 1.33/1.10 tff(k1_zfmisc_1_type, type, (
% 1.33/1.10 k1_zfmisc_1: $i > $i)).
% 1.33/1.10 tff(u1_struct_0_type, type, (
% 1.33/1.10 u1_struct_0: $i > $i)).
% 1.33/1.10 tff(k2_yellow_1_type, type, (
% 1.33/1.10 k2_yellow_1: $i > $i)).
% 1.33/1.10 tff(k8_waybel_0_type, type, (
% 1.33/1.10 k8_waybel_0: $i > $i)).
% 1.33/1.10 tff(g1_orders_2_type, type, (
% 1.33/1.10 g1_orders_2: ( $i * $i ) > $i)).
% 1.33/1.10 tff(k6_relset_1_type, type, (
% 1.33/1.10 k6_relset_1: ( $i * $i * $i ) > $i)).
% 1.33/1.10 tff(u1_orders_2_type, type, (
% 1.33/1.10 u1_orders_2: $i > $i)).
% 1.33/1.10 tff(tptp_fun_A_0_type, type, (
% 1.33/1.10 tptp_fun_A_0: $i)).
% 1.33/1.10 tff(tptp_fun_B_1_type, type, (
% 1.33/1.10 tptp_fun_B_1: $i)).
% 1.33/1.10 tff(k9_waybel_0_type, type, (
% 1.33/1.10 k9_waybel_0: $i > $i)).
% 1.33/1.10 tff(k7_lattice3_type, type, (
% 1.33/1.10 k7_lattice3: $i > $i)).
% 1.33/1.10 tff(v3_struct_0_type, type, (
% 1.33/1.10 v3_struct_0: $i > $o)).
% 1.33/1.10 tff(v2_lattice3_type, type, (
% 1.33/1.10 v2_lattice3: $i > $o)).
% 1.33/1.10 tff(l1_orders_2_type, type, (
% 1.33/1.10 l1_orders_2: $i > $o)).
% 1.33/1.10 tff(k3_tarski_type, type, (
% 1.33/1.10 k3_tarski: $i > $i)).
% 1.33/1.10 tff(k1_yellow_0_type, type, (
% 1.33/1.10 k1_yellow_0: ( $i * $i ) > $i)).
% 1.33/1.10 tff(v1_waybel_0_type, type, (
% 1.33/1.10 v1_waybel_0: ( $i * $i ) > $o)).
% 1.33/1.10 tff(v1_xboole_0_type, type, (
% 1.33/1.10 v1_xboole_0: $i > $o)).
% 1.33/1.10 tff(v2_yellow_0_type, type, (
% 1.33/1.10 v2_yellow_0: $i > $o)).
% 1.33/1.10 tff(v4_orders_2_type, type, (
% 1.33/1.10 v4_orders_2: $i > $o)).
% 1.33/1.10 tff(v3_orders_2_type, type, (
% 1.33/1.10 v3_orders_2: $i > $o)).
% 1.33/1.10 tff(v2_orders_2_type, type, (
% 1.33/1.10 v2_orders_2: $i > $o)).
% 1.33/1.10 tff(v1_orders_2_type, type, (
% 1.33/1.10 v1_orders_2: $i > $o)).
% 1.33/1.10 tff(v1_yellow_0_type, type, (
% 1.33/1.10 v1_yellow_0: $i > $o)).
% 1.33/1.10 tff(v1_lattice3_type, type, (
% 1.33/1.10 v1_lattice3: $i > $o)).
% 1.33/1.10 tff(1,plain,
% 1.33/1.10 (^[A: $i] : refl(((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(2,plain,
% 1.33/1.10 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[1])).
% 1.33/1.10 tff(3,plain,
% 1.33/1.10 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(4,plain,
% 1.33/1.10 (^[A: $i] : trans(monotonicity(rewrite((v2_lattice3(A) => (~v3_struct_0(A))) <=> ((~v2_lattice3(A)) | (~v3_struct_0(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> (l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))))), rewrite((l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(5,plain,
% 1.33/1.10 (![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[4])).
% 1.33/1.10 tff(6,axiom,(![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc2_lattice3')).
% 1.33/1.10 tff(7,plain,
% 1.33/1.10 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.33/1.10 tff(8,plain,
% 1.33/1.10 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.33/1.10 tff(9,plain,(
% 1.33/1.10 ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(skolemize,[status(sab)],[8])).
% 1.33/1.10 tff(10,plain,
% 1.33/1.10 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.33/1.10 tff(11,plain,
% 1.33/1.10 (((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0)) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))))) <=> (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(12,plain,
% 1.33/1.10 ((~(~(v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0)))) <=> (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(13,plain,
% 1.33/1.10 (((~(~(v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0)))) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))))) <=> ((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0)) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)))))),
% 1.33/1.10 inference(monotonicity,[status(thm)],[12])).
% 1.33/1.10 tff(14,plain,
% 1.33/1.10 (((~(~(v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0)))) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))))) <=> (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)))))),
% 1.33/1.10 inference(transitivity,[status(thm)],[13, 11])).
% 1.33/1.10 tff(15,plain,
% 1.33/1.10 ((~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B)))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(16,plain,
% 1.33/1.10 ((~![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v2_yellow_0(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B)))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(17,axiom,(~![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v2_yellow_0(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_waybel22')).
% 1.33/1.11 tff(18,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.33/1.11 tff(19,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[18, 15])).
% 1.33/1.11 tff(20,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.33/1.11 tff(21,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[20, 15])).
% 1.33/1.11 tff(22,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[21, 15])).
% 1.33/1.11 tff(23,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[22, 15])).
% 1.33/1.11 tff(24,plain,
% 1.33/1.11 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k9_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[23, 15])).
% 1.33/1.11 tff(25,plain,
% 1.33/1.11 (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v2_yellow_0(A!0) & v2_lattice3(A!0) & l1_orders_2(A!0) & (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[24, 14])).
% 1.33/1.11 tff(26,plain,
% 1.33/1.11 (l1_orders_2(A!0)),
% 1.33/1.11 inference(and_elim,[status(thm)],[25])).
% 1.33/1.11 tff(27,plain,
% 1.33/1.11 (v2_lattice3(A!0)),
% 1.33/1.11 inference(and_elim,[status(thm)],[25])).
% 1.33/1.11 tff(28,plain,
% 1.33/1.11 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(29,plain,
% 1.33/1.11 (((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0))) <=> ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(30,plain,
% 1.33/1.11 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))))),
% 1.33/1.11 inference(monotonicity,[status(thm)],[29])).
% 1.33/1.11 tff(31,plain,
% 1.33/1.11 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 1.33/1.11 inference(transitivity,[status(thm)],[30, 28])).
% 1.33/1.11 tff(32,plain,
% 1.33/1.11 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))),
% 1.33/1.11 inference(quant_inst,[status(thm)],[])).
% 1.33/1.11 tff(33,plain,
% 1.33/1.11 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.33/1.11 tff(34,plain,
% 1.33/1.11 (~v3_struct_0(A!0)),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[33, 27, 26, 10])).
% 1.33/1.11 tff(35,plain,
% 1.33/1.11 (^[A: $i] : refl((v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) <=> (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(36,plain,
% 1.33/1.11 (![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) <=> ![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[35])).
% 1.33/1.11 tff(37,plain,
% 1.33/1.11 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(38,plain,
% 1.33/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[37])).
% 1.33/1.11 tff(39,plain,
% 1.33/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(40,plain,
% 1.33/1.11 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A)) & l1_orders_2(A)))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)))), ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))), ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(41,plain,
% 1.33/1.11 (![A: $i] : (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[40])).
% 1.33/1.11 tff(42,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & l1_orders_2(A)) => (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_waybel16')).
% 1.33/1.11 tff(43,plain,
% 1.33/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.33/1.11 tff(44,plain,
% 1.33/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.33/1.11 tff(45,plain,(
% 1.33/1.11 ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A))) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))))),
% 1.33/1.11 inference(skolemize,[status(sab)],[44])).
% 1.33/1.11 tff(46,plain,
% 1.33/1.11 (![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.33/1.11 tff(47,plain,
% 1.33/1.11 (![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[46, 36])).
% 1.33/1.11 tff(48,plain,
% 1.33/1.11 (v3_orders_2(A!0)),
% 1.33/1.11 inference(and_elim,[status(thm)],[25])).
% 1.33/1.11 tff(49,plain,
% 1.33/1.11 (v2_orders_2(A!0)),
% 1.33/1.11 inference(and_elim,[status(thm)],[25])).
% 1.33/1.11 tff(50,plain,
% 1.33/1.11 (((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(51,plain,
% 1.33/1.11 ((v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0))) <=> ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(52,plain,
% 1.33/1.11 (((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0)))))),
% 1.33/1.11 inference(monotonicity,[status(thm)],[51])).
% 1.33/1.11 tff(53,plain,
% 1.33/1.11 (((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))))),
% 1.33/1.11 inference(transitivity,[status(thm)],[52, 50])).
% 1.33/1.11 tff(54,plain,
% 1.33/1.11 ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)))),
% 1.33/1.11 inference(quant_inst,[status(thm)],[])).
% 1.33/1.11 tff(55,plain,
% 1.33/1.11 ((~![A: $i] : (v3_struct_0(A) | (k9_waybel_0(A) = k8_waybel_0(k7_lattice3(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0)))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.33/1.11 tff(56,plain,
% 1.33/1.11 (v3_struct_0(A!0) | (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0)))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[55, 49, 48, 26, 47])).
% 1.33/1.11 tff(57,plain,
% 1.33/1.11 (k9_waybel_0(A!0) = k8_waybel_0(k7_lattice3(A!0))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[56, 34])).
% 1.33/1.11 tff(58,plain,
% 1.33/1.11 (k8_waybel_0(k7_lattice3(A!0)) = k9_waybel_0(A!0)),
% 1.33/1.11 inference(symmetry,[status(thm)],[57])).
% 1.33/1.11 tff(59,plain,
% 1.33/1.11 (^[A: $i] : refl(((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(60,plain,
% 1.33/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[59])).
% 1.33/1.11 tff(61,plain,
% 1.33/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(62,plain,
% 1.33/1.11 (^[A: $i] : rewrite((l1_orders_2(A) => (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(63,plain,
% 1.33/1.11 (![A: $i] : (l1_orders_2(A) => (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[62])).
% 1.33/1.11 tff(64,axiom,(![A: $i] : (l1_orders_2(A) => (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_lattice3')).
% 1.33/1.11 tff(65,plain,
% 1.33/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.33/1.11 tff(66,plain,
% 1.33/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[65, 61])).
% 1.33/1.11 tff(67,plain,(
% 1.33/1.11 ![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(skolemize,[status(sab)],[66])).
% 1.33/1.11 tff(68,plain,
% 1.33/1.11 (![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.33/1.11 tff(69,plain,
% 1.33/1.11 (((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | ((~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | (~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(70,plain,
% 1.33/1.11 ((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | ((~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))),
% 1.33/1.11 inference(quant_inst,[status(thm)],[])).
% 1.33/1.11 tff(71,plain,
% 1.33/1.11 ((~![A: $i] : ((~l1_orders_2(A)) | (k7_lattice3(A) = g1_orders_2(u1_struct_0(A), k6_relset_1(u1_struct_0(A), u1_struct_0(A), u1_orders_2(A)))))) | (~l1_orders_2(A!0)) | (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.33/1.11 tff(72,plain,
% 1.33/1.11 (k7_lattice3(A!0) = g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[71, 26, 68])).
% 1.33/1.11 tff(73,plain,
% 1.33/1.11 (g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))) = k7_lattice3(A!0)),
% 1.33/1.11 inference(symmetry,[status(thm)],[72])).
% 1.33/1.11 tff(74,plain,
% 1.33/1.11 (k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) = k8_waybel_0(k7_lattice3(A!0))),
% 1.33/1.11 inference(monotonicity,[status(thm)],[73])).
% 1.33/1.11 tff(75,plain,
% 1.33/1.11 (k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) = k9_waybel_0(A!0)),
% 1.33/1.11 inference(transitivity,[status(thm)],[74, 58])).
% 1.33/1.11 tff(76,plain,
% 1.33/1.11 (k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) = k2_yellow_1(k9_waybel_0(A!0))),
% 1.33/1.11 inference(monotonicity,[status(thm)],[75])).
% 1.33/1.11 tff(77,plain,
% 1.33/1.11 (u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))) = u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))),
% 1.33/1.11 inference(monotonicity,[status(thm)],[76])).
% 1.33/1.11 tff(78,plain,
% 1.33/1.11 (k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) = k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[77])).
% 1.33/1.12 tff(79,plain,
% 1.33/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))) <=> m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[78])).
% 1.33/1.12 tff(80,plain,
% 1.33/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))) <=> m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))),
% 1.33/1.12 inference(symmetry,[status(thm)],[79])).
% 1.33/1.12 tff(81,plain,
% 1.33/1.12 (~((~((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0))))))) | (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)))),
% 1.33/1.12 inference(and_elim,[status(thm)],[25])).
% 1.33/1.12 tff(82,plain,
% 1.33/1.12 ((~v1_xboole_0(B!1)) & v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))))),
% 1.33/1.12 inference(or_elim,[status(thm)],[81])).
% 1.33/1.12 tff(83,plain,
% 1.33/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A!0)))))),
% 1.33/1.12 inference(and_elim,[status(thm)],[82])).
% 1.33/1.12 tff(84,plain,
% 1.33/1.12 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[83, 80])).
% 1.33/1.12 tff(85,plain,
% 1.33/1.12 (v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))) <=> v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0)))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[76])).
% 1.33/1.12 tff(86,plain,
% 1.33/1.12 (v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0))) <=> v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))),
% 1.33/1.12 inference(symmetry,[status(thm)],[85])).
% 1.33/1.12 tff(87,plain,
% 1.33/1.12 (v1_waybel_0(B!1, k2_yellow_1(k9_waybel_0(A!0)))),
% 1.33/1.12 inference(and_elim,[status(thm)],[82])).
% 1.33/1.12 tff(88,plain,
% 1.33/1.12 (v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.33/1.12 tff(89,plain,
% 1.33/1.12 (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1)),
% 1.33/1.12 inference(monotonicity,[status(thm)],[76])).
% 1.33/1.12 tff(90,plain,
% 1.33/1.12 ((k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) <=> (k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[89])).
% 1.33/1.12 tff(91,plain,
% 1.33/1.12 ((k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1)) <=> (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1))),
% 1.33/1.12 inference(symmetry,[status(thm)],[90])).
% 1.33/1.12 tff(92,plain,
% 1.33/1.12 ((~(k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))) <=> (~(k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[91])).
% 1.33/1.12 tff(93,plain,
% 1.33/1.12 (~(k1_yellow_0(k2_yellow_1(k9_waybel_0(A!0)), B!1) = k3_tarski(B!1))),
% 1.33/1.12 inference(or_elim,[status(thm)],[81])).
% 1.33/1.12 tff(94,plain,
% 1.33/1.12 (~(k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.33/1.12 tff(95,plain,
% 1.33/1.12 (v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v2_orders_2(k7_lattice3(A!0))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[73])).
% 1.33/1.12 tff(96,plain,
% 1.33/1.12 (v2_orders_2(k7_lattice3(A!0)) <=> v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.12 inference(symmetry,[status(thm)],[95])).
% 1.33/1.12 tff(97,plain,
% 1.33/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(98,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[97])).
% 1.33/1.12 tff(99,plain,
% 1.33/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), rewrite((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))) <=> (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> (((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))))), rewrite((((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(100,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[99])).
% 1.33/1.12 tff(101,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(102,plain,
% 1.33/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)))), trans(monotonicity(rewrite(((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) <=> (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)))), ((((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))) <=> ((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))))), rewrite(((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))) <=> (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))), ((((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))) <=> (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A)))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(103,plain,
% 1.33/1.12 (![A: $i] : ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[102])).
% 1.33/1.12 tff(104,axiom,(![A: $i] : ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => (((v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A))) & v3_orders_2(k7_lattice3(A))) & v4_orders_2(k7_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_lattice3')).
% 1.33/1.12 tff(105,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.33/1.12 tff(106,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.33/1.12 tff(107,plain,(
% 1.33/1.12 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A))))),
% 1.33/1.12 inference(skolemize,[status(sab)],[106])).
% 1.33/1.12 tff(108,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[107, 100])).
% 1.33/1.12 tff(109,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[108, 98])).
% 1.33/1.12 tff(110,plain,
% 1.33/1.12 (v4_orders_2(A!0)),
% 1.33/1.12 inference(and_elim,[status(thm)],[25])).
% 1.33/1.12 tff(111,plain,
% 1.33/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(112,plain,
% 1.33/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))))),
% 1.33/1.12 inference(quant_inst,[status(thm)],[])).
% 1.33/1.12 tff(113,plain,
% 1.33/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v2_orders_2(k7_lattice3(A))) | (~v3_orders_2(k7_lattice3(A))) | (~v4_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.33/1.12 tff(114,plain,
% 1.33/1.12 (~((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0))))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[113, 49, 48, 110, 26, 109])).
% 1.33/1.12 tff(115,plain,
% 1.33/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))) | v2_orders_2(k7_lattice3(A!0))),
% 1.33/1.12 inference(tautology,[status(thm)],[])).
% 1.33/1.12 tff(116,plain,
% 1.33/1.12 (v2_orders_2(k7_lattice3(A!0))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.33/1.12 tff(117,plain,
% 1.33/1.12 (v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[116, 96])).
% 1.33/1.12 tff(118,plain,
% 1.33/1.12 (v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v1_yellow_0(k7_lattice3(A!0))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[73])).
% 1.33/1.12 tff(119,plain,
% 1.33/1.12 (v1_yellow_0(k7_lattice3(A!0)) <=> v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.12 inference(symmetry,[status(thm)],[118])).
% 1.33/1.12 tff(120,plain,
% 1.33/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(121,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[120])).
% 1.33/1.12 tff(122,plain,
% 1.33/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_yellow_0(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v2_yellow_0(A))))), ((~(v2_yellow_0(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v2_yellow_0(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v2_yellow_0(A))))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)))), ((~(v2_yellow_0(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A))))), rewrite((v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))) <=> (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))), (((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> (((~l1_orders_2(A)) | (~v2_yellow_0(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))))), rewrite((((~l1_orders_2(A)) | (~v2_yellow_0(A))) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))), (((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(123,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[122])).
% 1.33/1.12 tff(124,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(125,plain,
% 1.33/1.12 (^[A: $i] : rewrite(((v2_yellow_0(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(126,plain,
% 1.33/1.12 (![A: $i] : ((v2_yellow_0(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[125])).
% 1.33/1.12 tff(127,axiom,(![A: $i] : ((v2_yellow_0(A) & l1_orders_2(A)) => (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc10_yellow_7')).
% 1.33/1.12 tff(128,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.33/1.12 tff(129,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.33/1.12 tff(130,plain,(
% 1.33/1.12 ![A: $i] : ((~(v2_yellow_0(A) & l1_orders_2(A))) | (v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A))))),
% 1.33/1.12 inference(skolemize,[status(sab)],[129])).
% 1.33/1.12 tff(131,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[130, 123])).
% 1.33/1.12 tff(132,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[131, 121])).
% 1.33/1.12 tff(133,plain,
% 1.33/1.12 (v2_yellow_0(A!0)),
% 1.33/1.12 inference(and_elim,[status(thm)],[25])).
% 1.33/1.12 tff(134,plain,
% 1.33/1.12 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(135,plain,
% 1.33/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))))),
% 1.33/1.12 inference(quant_inst,[status(thm)],[])).
% 1.33/1.12 tff(136,plain,
% 1.33/1.12 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_yellow_0(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~v1_yellow_0(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_yellow_0(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0)))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.33/1.12 tff(137,plain,
% 1.33/1.12 (~((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0))))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[136, 133, 26, 132])).
% 1.33/1.12 tff(138,plain,
% 1.33/1.12 (((~v1_orders_2(k7_lattice3(A!0))) | (~v1_yellow_0(k7_lattice3(A!0)))) | v1_yellow_0(k7_lattice3(A!0))),
% 1.33/1.12 inference(tautology,[status(thm)],[])).
% 1.33/1.12 tff(139,plain,
% 1.33/1.12 (v1_yellow_0(k7_lattice3(A!0))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[138, 137])).
% 1.33/1.12 tff(140,plain,
% 1.33/1.12 (v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[139, 119])).
% 1.33/1.12 tff(141,plain,
% 1.33/1.12 (v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v1_lattice3(k7_lattice3(A!0))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[73])).
% 1.33/1.12 tff(142,plain,
% 1.33/1.12 (v1_lattice3(k7_lattice3(A!0)) <=> v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.12 inference(symmetry,[status(thm)],[141])).
% 1.33/1.12 tff(143,plain,
% 1.33/1.12 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(144,plain,
% 1.33/1.12 (![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[143])).
% 1.33/1.12 tff(145,plain,
% 1.33/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_lattice3(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v2_lattice3(A))))), ((~(v2_lattice3(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v2_lattice3(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v2_lattice3(A))))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)))), ((~(v2_lattice3(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A))))), rewrite(((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))) <=> (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))), (((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> (((~l1_orders_2(A)) | (~v2_lattice3(A))) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))))), rewrite((((~l1_orders_2(A)) | (~v2_lattice3(A))) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))), (((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(146,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[145])).
% 1.33/1.12 tff(147,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(148,plain,
% 1.33/1.12 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A))) <=> ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))), (((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A)))) <=> ((v2_lattice3(A) & l1_orders_2(A)) => ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))))), rewrite(((v2_lattice3(A) & l1_orders_2(A)) => ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)))) <=> ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))), (((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A)))) <=> ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))))),
% 1.33/1.12 inference(bind,[status(th)],[])).
% 1.33/1.12 tff(149,plain,
% 1.33/1.12 (![A: $i] : ((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A)))) <=> ![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 1.33/1.12 inference(quant_intro,[status(thm)],[148])).
% 1.33/1.12 tff(150,axiom,(![A: $i] : ((v2_lattice3(A) & l1_orders_2(A)) => (((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A))) & v1_lattice3(k7_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_yellow_7')).
% 1.33/1.12 tff(151,plain,
% 1.33/1.12 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.33/1.13 tff(152,plain,
% 1.33/1.13 (![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.33/1.13 tff(153,plain,(
% 1.33/1.13 ![A: $i] : ((~(v2_lattice3(A) & l1_orders_2(A))) | ((~v3_struct_0(k7_lattice3(A))) & v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A))))),
% 1.33/1.13 inference(skolemize,[status(sab)],[152])).
% 1.33/1.13 tff(154,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[153, 146])).
% 1.33/1.13 tff(155,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[154, 144])).
% 1.33/1.13 tff(156,plain,
% 1.33/1.13 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 1.33/1.13 inference(rewrite,[status(thm)],[])).
% 1.33/1.13 tff(157,plain,
% 1.33/1.13 (((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0)))))) <=> ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 1.33/1.13 inference(rewrite,[status(thm)],[])).
% 1.33/1.13 tff(158,plain,
% 1.33/1.13 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0)))))))),
% 1.33/1.13 inference(monotonicity,[status(thm)],[157])).
% 1.33/1.13 tff(159,plain,
% 1.33/1.13 (((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 1.33/1.13 inference(transitivity,[status(thm)],[158, 156])).
% 1.33/1.13 tff(160,plain,
% 1.33/1.13 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~(v3_struct_0(k7_lattice3(A!0)) | (~v1_orders_2(k7_lattice3(A!0))) | (~v1_lattice3(k7_lattice3(A!0))))))),
% 1.33/1.13 inference(quant_inst,[status(thm)],[])).
% 1.33/1.13 tff(161,plain,
% 1.33/1.13 ((~![A: $i] : ((~l1_orders_2(A)) | (~v2_lattice3(A)) | (~(v3_struct_0(k7_lattice3(A)) | (~v1_orders_2(k7_lattice3(A))) | (~v1_lattice3(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0)))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.33/1.13 tff(162,plain,
% 1.33/1.13 (~((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0))))),
% 1.33/1.13 inference(unit_resolution,[status(thm)],[161, 27, 26, 155])).
% 1.33/1.13 tff(163,plain,
% 1.33/1.13 (((~v1_orders_2(k7_lattice3(A!0))) | v3_struct_0(k7_lattice3(A!0)) | (~v1_lattice3(k7_lattice3(A!0)))) | v1_lattice3(k7_lattice3(A!0))),
% 1.33/1.13 inference(tautology,[status(thm)],[])).
% 1.33/1.13 tff(164,plain,
% 1.33/1.13 (v1_lattice3(k7_lattice3(A!0))),
% 1.33/1.13 inference(unit_resolution,[status(thm)],[163, 162])).
% 1.33/1.13 tff(165,plain,
% 1.33/1.13 (v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[164, 142])).
% 1.33/1.13 tff(166,plain,
% 1.33/1.13 (v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v4_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(monotonicity,[status(thm)],[73])).
% 1.33/1.13 tff(167,plain,
% 1.33/1.13 (v4_orders_2(k7_lattice3(A!0)) <=> v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(symmetry,[status(thm)],[166])).
% 1.33/1.13 tff(168,plain,
% 1.33/1.13 (((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))) | v4_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(tautology,[status(thm)],[])).
% 1.33/1.13 tff(169,plain,
% 1.33/1.13 (v4_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(unit_resolution,[status(thm)],[168, 114])).
% 1.33/1.13 tff(170,plain,
% 1.33/1.13 (v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[169, 167])).
% 1.33/1.13 tff(171,plain,
% 1.33/1.13 (v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))) <=> v3_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(monotonicity,[status(thm)],[73])).
% 1.33/1.13 tff(172,plain,
% 1.33/1.13 (v3_orders_2(k7_lattice3(A!0)) <=> v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(symmetry,[status(thm)],[171])).
% 1.33/1.13 tff(173,plain,
% 1.33/1.13 (((~v1_orders_2(k7_lattice3(A!0))) | (~v2_orders_2(k7_lattice3(A!0))) | (~v3_orders_2(k7_lattice3(A!0))) | (~v4_orders_2(k7_lattice3(A!0)))) | v3_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(tautology,[status(thm)],[])).
% 1.33/1.13 tff(174,plain,
% 1.33/1.13 (v3_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(unit_resolution,[status(thm)],[173, 114])).
% 1.33/1.13 tff(175,plain,
% 1.33/1.13 (v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[174, 172])).
% 1.33/1.13 tff(176,plain,
% 1.33/1.13 (l1_orders_2(k7_lattice3(A!0)) <=> l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(monotonicity,[status(thm)],[72])).
% 1.33/1.13 tff(177,plain,
% 1.33/1.13 (^[A: $i] : refl(((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))) <=> ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))))),
% 1.33/1.13 inference(bind,[status(th)],[])).
% 1.33/1.13 tff(178,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 1.33/1.13 inference(quant_intro,[status(thm)],[177])).
% 1.33/1.13 tff(179,plain,
% 1.33/1.13 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A)))))))),
% 1.33/1.13 inference(bind,[status(th)],[])).
% 1.33/1.13 tff(180,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 1.33/1.13 inference(quant_intro,[status(thm)],[179])).
% 1.33/1.13 tff(181,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 1.33/1.13 inference(rewrite,[status(thm)],[])).
% 1.33/1.13 tff(182,plain,
% 1.33/1.13 (^[A: $i] : rewrite((l1_orders_2(A) => (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))))),
% 1.33/1.13 inference(bind,[status(th)],[])).
% 1.33/1.13 tff(183,plain,
% 1.33/1.13 (![A: $i] : (l1_orders_2(A) => (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 1.33/1.13 inference(quant_intro,[status(thm)],[182])).
% 1.33/1.13 tff(184,axiom,(![A: $i] : (l1_orders_2(A) => (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_lattice3')).
% 1.33/1.13 tff(185,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.33/1.13 tff(186,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.33/1.13 tff(187,plain,(
% 1.33/1.13 ![A: $i] : ((~l1_orders_2(A)) | (v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A))))),
% 1.33/1.13 inference(skolemize,[status(sab)],[186])).
% 1.33/1.13 tff(188,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.33/1.13 tff(189,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[188, 178])).
% 1.33/1.13 tff(190,plain,
% 1.33/1.13 (((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))))),
% 1.33/1.13 inference(rewrite,[status(thm)],[])).
% 1.33/1.13 tff(191,plain,
% 1.33/1.13 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | ((~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))))),
% 1.33/1.13 inference(quant_inst,[status(thm)],[])).
% 1.33/1.13 tff(192,plain,
% 1.33/1.13 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_orders_2(k7_lattice3(A))) | (~l1_orders_2(k7_lattice3(A))))))) | (~l1_orders_2(A!0)) | (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0)))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.33/1.13 tff(193,plain,
% 1.33/1.13 (~((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0))))),
% 1.33/1.13 inference(unit_resolution,[status(thm)],[192, 26, 189])).
% 1.33/1.13 tff(194,plain,
% 1.33/1.13 (((~v1_orders_2(k7_lattice3(A!0))) | (~l1_orders_2(k7_lattice3(A!0)))) | l1_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(tautology,[status(thm)],[])).
% 1.33/1.13 tff(195,plain,
% 1.33/1.13 (l1_orders_2(k7_lattice3(A!0))),
% 1.33/1.13 inference(unit_resolution,[status(thm)],[194, 193])).
% 1.33/1.13 tff(196,plain,
% 1.33/1.13 (l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))),
% 1.33/1.13 inference(modus_ponens,[status(thm)],[195, 176])).
% 1.33/1.13 tff(197,plain,
% 1.33/1.13 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))),
% 1.33/1.13 inference(bind,[status(th)],[])).
% 1.33/1.13 tff(198,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 1.33/1.13 inference(quant_intro,[status(thm)],[197])).
% 1.33/1.13 tff(199,plain,
% 1.33/1.13 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))),
% 1.33/1.13 inference(bind,[status(th)],[])).
% 1.33/1.13 tff(200,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 1.33/1.13 inference(quant_intro,[status(thm)],[199])).
% 1.33/1.13 tff(201,plain,
% 1.33/1.13 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 1.33/1.13 inference(transitivity,[status(thm)],[200, 198])).
% 1.33/1.13 tff(202,plain,
% 1.33/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) <=> (~(v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) <=> (~(~(v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) <=> (v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))), ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) <=> (v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), (((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ((v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), rewrite(((v1_xboole_0(B) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))), (((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> (((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))))), rewrite((((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))))),
% 1.33/1.13 inference(bind,[status(th)],[])).
% 1.33/1.13 tff(203,plain,
% 1.33/1.13 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 1.33/1.13 inference(quant_intro,[status(thm)],[202])).
% 1.33/1.13 tff(204,plain,
% 1.33/1.13 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.13 inference(rewrite,[status(thm)],[])).
% 1.33/1.13 tff(205,plain,
% 1.33/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v1_yellow_0(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v1_yellow_0(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A)))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) <=> ((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))), (((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> (((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), rewrite((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))), (((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))))), (![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))))),
% 1.33/1.14 inference(bind,[status(th)],[])).
% 1.33/1.14 tff(206,plain,
% 1.33/1.14 (![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.14 inference(quant_intro,[status(thm)],[205])).
% 1.33/1.14 tff(207,axiom,(![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v1_yellow_0(A)) & l1_orders_2(A)) => ![B: $i] : ((((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) => (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_waybel13')).
% 1.33/1.14 tff(208,plain,
% 1.33/1.14 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.33/1.14 tff(209,plain,
% 1.33/1.14 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.33/1.14 tff(210,plain,(
% 1.33/1.14 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B))))),
% 1.33/1.14 inference(skolemize,[status(sab)],[209])).
% 1.33/1.14 tff(211,plain,
% 1.33/1.14 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.33/1.14 tff(212,plain,
% 1.33/1.14 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))),
% 1.33/1.14 inference(modus_ponens,[status(thm)],[211, 201])).
% 1.33/1.14 tff(213,plain,
% 1.33/1.14 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(214,plain,
% 1.33/1.14 (((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) <=> ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 1.33/1.14 inference(rewrite,[status(thm)],[])).
% 1.33/1.14 tff(215,plain,
% 1.33/1.14 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))))),
% 1.33/1.14 inference(monotonicity,[status(thm)],[214])).
% 1.33/1.14 tff(216,plain,
% 1.33/1.14 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 1.33/1.14 inference(transitivity,[status(thm)],[215, 213])).
% 1.33/1.14 tff(217,plain,
% 1.33/1.14 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))))),
% 1.33/1.15 inference(quant_inst,[status(thm)],[])).
% 1.33/1.15 tff(218,plain,
% 1.33/1.15 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_orders_2(A)) | (~v1_yellow_0(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(A)), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))))))) | (~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 1.33/1.15 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.33/1.15 tff(219,plain,
% 1.33/1.15 ((~l1_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v2_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v3_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v4_orders_2(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_lattice3(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | (~v1_yellow_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))) | ![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 1.33/1.15 inference(unit_resolution,[status(thm)],[218, 212])).
% 1.33/1.15 tff(220,plain,
% 1.33/1.15 (![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 1.41/1.15 inference(unit_resolution,[status(thm)],[219, 196, 175, 170, 165, 140, 117])).
% 1.41/1.15 tff(221,plain,
% 1.41/1.15 (~v1_xboole_0(B!1)),
% 1.41/1.15 inference(and_elim,[status(thm)],[82])).
% 1.41/1.15 tff(222,plain,
% 1.41/1.15 (((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | (v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(223,plain,
% 1.41/1.15 ((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | (v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))),
% 1.41/1.15 inference(quant_inst,[status(thm)],[])).
% 1.41/1.15 tff(224,plain,
% 1.41/1.15 ((~![B: $i] : (v1_xboole_0(B) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B) = k3_tarski(B)) | (~v1_waybel_0(B, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))))))) | v1_xboole_0(B!1) | (k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.41/1.17 tff(225,plain,
% 1.41/1.17 ((k1_yellow_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))), B!1) = k3_tarski(B!1)) | (~v1_waybel_0(B!1, k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(g1_orders_2(u1_struct_0(A!0), k6_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_orders_2(A!0)))))))))),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[224, 221, 220])).
% 1.41/1.17 tff(226,plain,
% 1.41/1.17 ($false),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[225, 94, 88, 84])).
% 1.41/1.17 % SZS output end Proof
%------------------------------------------------------------------------------