TSTP Solution File: LAT298+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT298+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 18:32:49 EDT 2022
% Result : Theorem 80.52s 50.91s
% Output : Proof 80.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT298+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Sep 1 13:48:18 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 80.52/50.91 % SZS status Theorem
% 80.52/50.91 % SZS output start Proof
% 80.52/50.91 tff(r2_hidden_type, type, (
% 80.52/50.91 r2_hidden: ( $i * $i ) > $o)).
% 80.52/50.91 tff(tptp_fun_C_2_type, type, (
% 80.52/50.91 tptp_fun_C_2: $i)).
% 80.52/50.91 tff(k4_lattices_type, type, (
% 80.52/50.91 k4_lattices: ( $i * $i * $i ) > $i)).
% 80.52/50.91 tff(tptp_fun_C_3_type, type, (
% 80.52/50.91 tptp_fun_C_3: ( $i * $i ) > $i)).
% 80.52/50.91 tff(tptp_fun_B_1_type, type, (
% 80.52/50.91 tptp_fun_B_1: $i)).
% 80.52/50.91 tff(tptp_fun_D_4_type, type, (
% 80.52/50.91 tptp_fun_D_4: ( $i * $i ) > $i)).
% 80.52/50.91 tff(tptp_fun_A_0_type, type, (
% 80.52/50.91 tptp_fun_A_0: $i)).
% 80.52/50.91 tff(m1_subset_1_type, type, (
% 80.52/50.91 m1_subset_1: ( $i * $i ) > $o)).
% 80.52/50.91 tff(u1_struct_0_type, type, (
% 80.52/50.91 u1_struct_0: $i > $i)).
% 80.52/50.91 tff(m1_filter_0_type, type, (
% 80.52/50.91 m1_filter_0: ( $i * $i ) > $o)).
% 80.52/50.91 tff(k1_zfmisc_1_type, type, (
% 80.52/50.91 k1_zfmisc_1: $i > $i)).
% 80.52/50.91 tff(u1_lattices_type, type, (
% 80.52/50.91 u1_lattices: $i > $i)).
% 80.52/50.91 tff(u2_lattices_type, type, (
% 80.52/50.91 u2_lattices: $i > $i)).
% 80.52/50.91 tff(g3_lattices_type, type, (
% 80.52/50.91 g3_lattices: ( $i * $i * $i ) > $i)).
% 80.52/50.91 tff(l3_lattices_type, type, (
% 80.52/50.91 l3_lattices: $i > $o)).
% 80.52/50.91 tff(v10_lattices_type, type, (
% 80.52/50.91 v10_lattices: $i > $o)).
% 80.52/50.91 tff(v3_struct_0_type, type, (
% 80.52/50.91 v3_struct_0: $i > $o)).
% 80.52/50.91 tff(m1_filter_2_type, type, (
% 80.52/50.91 m1_filter_2: ( $i * $i ) > $o)).
% 80.52/50.91 tff(m1_relset_1_type, type, (
% 80.52/50.91 m1_relset_1: ( $i * $i * $i ) > $o)).
% 80.52/50.91 tff(k2_zfmisc_1_type, type, (
% 80.52/50.91 k2_zfmisc_1: ( $i * $i ) > $i)).
% 80.52/50.91 tff(m2_relset_1_type, type, (
% 80.52/50.91 m2_relset_1: ( $i * $i * $i ) > $o)).
% 80.52/50.91 tff(v1_funct_2_type, type, (
% 80.52/50.91 v1_funct_2: ( $i * $i * $i ) > $o)).
% 80.52/50.91 tff(v1_funct_1_type, type, (
% 80.52/50.91 v1_funct_1: $i > $o)).
% 80.52/50.91 tff(l1_lattices_type, type, (
% 80.52/50.91 l1_lattices: $i > $o)).
% 80.52/50.91 tff(l2_lattices_type, type, (
% 80.52/50.91 l2_lattices: $i > $o)).
% 80.52/50.91 tff(m2_lattice4_type, type, (
% 80.52/50.91 m2_lattice4: ( $i * $i ) > $o)).
% 80.52/50.91 tff(v1_xboole_0_type, type, (
% 80.52/50.91 v1_xboole_0: $i > $o)).
% 80.52/50.91 tff(v6_lattices_type, type, (
% 80.52/50.91 v6_lattices: $i > $o)).
% 80.52/50.91 tff(v9_lattices_type, type, (
% 80.52/50.91 v9_lattices: $i > $o)).
% 80.52/50.91 tff(v8_lattices_type, type, (
% 80.52/50.91 v8_lattices: $i > $o)).
% 80.52/50.91 tff(v7_lattices_type, type, (
% 80.52/50.91 v7_lattices: $i > $o)).
% 80.52/50.91 tff(v5_lattices_type, type, (
% 80.52/50.91 v5_lattices: $i > $o)).
% 80.52/50.91 tff(v4_lattices_type, type, (
% 80.52/50.91 v4_lattices: $i > $o)).
% 80.52/50.91 tff(k2_lattices_type, type, (
% 80.52/50.91 k2_lattices: ( $i * $i * $i ) > $i)).
% 80.52/50.91 tff(k2_binop_1_type, type, (
% 80.52/50.91 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 80.52/50.91 tff(1,plain,
% 80.52/50.91 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(2,plain,
% 80.52/50.91 (((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))) <=> ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(3,plain,
% 80.52/50.91 ((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(4,plain,
% 80.52/50.91 ((~(~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))) <=> (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(5,plain,
% 80.52/50.91 (((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (~(~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))) & (~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))))) <=> ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))),
% 80.52/50.91 inference(monotonicity,[status(thm)],[4, 3])).
% 80.52/50.91 tff(6,plain,
% 80.52/50.91 (((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (~(~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))) & (~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))))) <=> ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 80.52/50.91 inference(transitivity,[status(thm)],[5, 2])).
% 80.52/50.91 tff(7,plain,
% 80.52/50.91 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(8,plain,
% 80.52/50.91 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (~(~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))) & (~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))),
% 80.52/50.91 inference(monotonicity,[status(thm)],[7, 6])).
% 80.52/50.91 tff(9,plain,
% 80.52/50.91 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (~(~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))) & (~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 80.52/50.91 inference(transitivity,[status(thm)],[8, 1])).
% 80.52/50.91 tff(10,plain,
% 80.52/50.91 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(11,plain,
% 80.52/50.91 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_filter_2(C, A) => m1_filter_2(C, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(12,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_filter_2(C, A) => m1_filter_2(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_filter_2')).
% 80.52/50.91 tff(13,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[12, 11])).
% 80.52/50.91 tff(14,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[13, 10])).
% 80.52/50.91 tff(15,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[14, 10])).
% 80.52/50.91 tff(16,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[15, 10])).
% 80.52/50.91 tff(17,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[16, 10])).
% 80.52/50.91 tff(18,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[17, 10])).
% 80.52/50.91 tff(19,plain,
% 80.52/50.91 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[18, 10])).
% 80.52/50.91 tff(20,plain,
% 80.52/50.91 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[19, 9])).
% 80.52/50.91 tff(21,plain,
% 80.52/50.91 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))),
% 80.52/50.91 inference(and_elim,[status(thm)],[20])).
% 80.52/50.91 tff(22,plain,
% 80.52/50.91 (g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 80.52/50.91 inference(symmetry,[status(thm)],[21])).
% 80.52/50.91 tff(23,plain,
% 80.52/50.91 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(24,plain,
% 80.52/50.91 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[23])).
% 80.52/50.91 tff(25,plain,
% 80.52/50.91 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(26,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 80.52/50.91 tff(27,plain,
% 80.52/50.91 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[26, 25])).
% 80.52/50.91 tff(28,plain,(
% 80.52/50.91 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 80.52/50.91 inference(skolemize,[status(sab)],[27])).
% 80.52/50.91 tff(29,plain,
% 80.52/50.91 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[28, 24])).
% 80.52/50.91 tff(30,plain,
% 80.52/50.91 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 80.52/50.91 inference(quant_inst,[status(thm)],[])).
% 80.52/50.91 tff(31,plain,
% 80.52/50.91 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.52/50.91 inference(unit_resolution,[status(thm)],[30, 29])).
% 80.52/50.91 tff(32,plain,
% 80.52/50.91 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(33,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[32])).
% 80.52/50.91 tff(34,plain,
% 80.52/50.91 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(35,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[34])).
% 80.52/50.91 tff(36,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(37,plain,
% 80.52/50.91 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(38,plain,
% 80.52/50.91 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[37])).
% 80.52/50.91 tff(39,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 80.52/50.91 tff(40,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[39, 38])).
% 80.52/50.91 tff(41,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[40, 36])).
% 80.52/50.91 tff(42,plain,(
% 80.52/50.91 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 80.52/50.91 inference(skolemize,[status(sab)],[41])).
% 80.52/50.91 tff(43,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[42, 35])).
% 80.52/50.91 tff(44,plain,
% 80.52/50.91 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[43, 33])).
% 80.52/50.91 tff(45,plain,
% 80.52/50.91 (l3_lattices(B!1)),
% 80.52/50.91 inference(and_elim,[status(thm)],[20])).
% 80.52/50.91 tff(46,plain,
% 80.52/50.91 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(47,plain,
% 80.52/50.91 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 80.52/50.91 inference(quant_inst,[status(thm)],[])).
% 80.52/50.91 tff(48,plain,
% 80.52/50.91 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[47, 46])).
% 80.52/50.91 tff(49,plain,
% 80.52/50.91 (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))),
% 80.52/50.91 inference(unit_resolution,[status(thm)],[48, 45, 44])).
% 80.52/50.91 tff(50,plain,
% 80.52/50.91 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l1_lattices(B!1)),
% 80.52/50.91 inference(tautology,[status(thm)],[])).
% 80.52/50.91 tff(51,plain,
% 80.52/50.91 (l1_lattices(B!1)),
% 80.52/50.91 inference(unit_resolution,[status(thm)],[50, 49])).
% 80.52/50.91 tff(52,plain,
% 80.52/50.91 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(53,plain,
% 80.52/50.91 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[52])).
% 80.52/50.91 tff(54,plain,
% 80.52/50.91 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(55,plain,
% 80.52/50.91 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[54])).
% 80.52/50.91 tff(56,plain,
% 80.52/50.91 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.52/50.91 inference(rewrite,[status(thm)],[])).
% 80.52/50.91 tff(57,plain,
% 80.52/50.91 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.52/50.91 inference(bind,[status(th)],[])).
% 80.52/50.91 tff(58,plain,
% 80.52/50.91 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.52/50.91 inference(quant_intro,[status(thm)],[57])).
% 80.52/50.91 tff(59,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 80.52/50.91 tff(60,plain,
% 80.52/50.91 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[59, 58])).
% 80.52/50.91 tff(61,plain,
% 80.52/50.91 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.52/50.91 inference(modus_ponens,[status(thm)],[60, 56])).
% 80.52/50.91 tff(62,plain,(
% 80.52/50.91 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.52/50.91 inference(skolemize,[status(sab)],[61])).
% 80.52/50.91 tff(63,plain,
% 80.52/50.91 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.91 inference(modus_ponens,[status(thm)],[62, 55])).
% 80.64/50.91 tff(64,plain,
% 80.64/50.91 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.91 inference(modus_ponens,[status(thm)],[63, 53])).
% 80.64/50.91 tff(65,plain,
% 80.64/50.91 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 80.64/50.91 inference(rewrite,[status(thm)],[])).
% 80.64/50.91 tff(66,plain,
% 80.64/50.91 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 80.64/50.91 inference(quant_inst,[status(thm)],[])).
% 80.64/50.91 tff(67,plain,
% 80.64/50.91 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 80.64/50.91 inference(modus_ponens,[status(thm)],[66, 65])).
% 80.64/50.91 tff(68,plain,
% 80.64/50.91 ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[67, 64])).
% 80.64/50.91 tff(69,plain,
% 80.64/50.91 (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[68, 51])).
% 80.64/50.91 tff(70,plain,
% 80.64/50.91 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(tautology,[status(thm)],[])).
% 80.64/50.91 tff(71,plain,
% 80.64/50.91 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[70, 69])).
% 80.64/50.91 tff(72,plain,
% 80.64/50.91 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(tautology,[status(thm)],[])).
% 80.64/50.91 tff(73,plain,
% 80.64/50.91 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[72, 71])).
% 80.64/50.91 tff(74,plain,
% 80.64/50.91 (m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[73, 31])).
% 80.64/50.91 tff(75,plain,
% 80.64/50.91 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(tautology,[status(thm)],[])).
% 80.64/50.91 tff(76,plain,
% 80.64/50.91 (v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[75, 69])).
% 80.64/50.91 tff(77,plain,
% 80.64/50.91 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u1_lattices(B!1))),
% 80.64/50.91 inference(tautology,[status(thm)],[])).
% 80.64/50.91 tff(78,plain,
% 80.64/50.91 (v1_funct_1(u1_lattices(B!1))),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[77, 69])).
% 80.64/50.91 tff(79,plain,
% 80.64/50.91 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l2_lattices(B!1)),
% 80.64/50.91 inference(tautology,[status(thm)],[])).
% 80.64/50.91 tff(80,plain,
% 80.64/50.91 (l2_lattices(B!1)),
% 80.64/50.91 inference(unit_resolution,[status(thm)],[79, 49])).
% 80.64/50.91 tff(81,plain,
% 80.64/50.91 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 80.64/50.91 inference(bind,[status(th)],[])).
% 80.64/50.91 tff(82,plain,
% 80.64/50.91 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.91 inference(quant_intro,[status(thm)],[81])).
% 80.64/50.91 tff(83,plain,
% 80.64/50.91 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 80.64/50.91 inference(bind,[status(th)],[])).
% 80.64/50.91 tff(84,plain,
% 80.64/50.91 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.91 inference(quant_intro,[status(thm)],[83])).
% 80.64/50.91 tff(85,plain,
% 80.64/50.91 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.64/50.91 inference(rewrite,[status(thm)],[])).
% 80.64/50.91 tff(86,plain,
% 80.64/50.91 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.91 inference(bind,[status(th)],[])).
% 80.64/50.91 tff(87,plain,
% 80.64/50.91 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.64/50.91 inference(quant_intro,[status(thm)],[86])).
% 80.64/50.91 tff(88,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 80.64/50.91 tff(89,plain,
% 80.64/50.91 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.64/50.91 inference(modus_ponens,[status(thm)],[88, 87])).
% 80.64/50.91 tff(90,plain,
% 80.64/50.92 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[89, 85])).
% 80.64/50.92 tff(91,plain,(
% 80.64/50.92 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 80.64/50.92 inference(skolemize,[status(sab)],[90])).
% 80.64/50.92 tff(92,plain,
% 80.64/50.92 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[91, 84])).
% 80.64/50.92 tff(93,plain,
% 80.64/50.92 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[92, 82])).
% 80.64/50.92 tff(94,plain,
% 80.64/50.92 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 80.64/50.92 inference(rewrite,[status(thm)],[])).
% 80.64/50.92 tff(95,plain,
% 80.64/50.92 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 80.64/50.92 inference(quant_inst,[status(thm)],[])).
% 80.64/50.92 tff(96,plain,
% 80.64/50.92 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[95, 94])).
% 80.64/50.92 tff(97,plain,
% 80.64/50.92 ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[96, 93])).
% 80.64/50.92 tff(98,plain,
% 80.64/50.92 (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[97, 80])).
% 80.64/50.92 tff(99,plain,
% 80.64/50.92 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(tautology,[status(thm)],[])).
% 80.64/50.92 tff(100,plain,
% 80.64/50.92 (v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[99, 98])).
% 80.64/50.92 tff(101,plain,
% 80.64/50.92 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u2_lattices(B!1))),
% 80.64/50.92 inference(tautology,[status(thm)],[])).
% 80.64/50.92 tff(102,plain,
% 80.64/50.92 (v1_funct_1(u2_lattices(B!1))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[101, 98])).
% 80.64/50.92 tff(103,plain,
% 80.64/50.92 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 80.64/50.92 inference(quant_inst,[status(thm)],[])).
% 80.64/50.92 tff(104,plain,
% 80.64/50.92 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[103, 29])).
% 80.64/50.92 tff(105,plain,
% 80.64/50.92 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(tautology,[status(thm)],[])).
% 80.64/50.92 tff(106,plain,
% 80.64/50.92 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[105, 98])).
% 80.64/50.92 tff(107,plain,
% 80.64/50.92 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(tautology,[status(thm)],[])).
% 80.64/50.92 tff(108,plain,
% 80.64/50.92 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[107, 106])).
% 80.64/50.92 tff(109,plain,
% 80.64/50.92 (m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[108, 104])).
% 80.64/50.92 tff(110,plain,
% 80.64/50.92 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(111,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[110])).
% 80.64/50.92 tff(112,plain,
% 80.64/50.92 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(113,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[112])).
% 80.64/50.92 tff(114,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 80.64/50.92 inference(transitivity,[status(thm)],[113, 111])).
% 80.64/50.92 tff(115,plain,
% 80.64/50.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(116,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[115])).
% 80.64/50.92 tff(117,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 80.64/50.92 inference(rewrite,[status(thm)],[])).
% 80.64/50.92 tff(118,plain,
% 80.64/50.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(119,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[118])).
% 80.64/50.92 tff(120,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 80.64/50.92 tff(121,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[120, 119])).
% 80.64/50.92 tff(122,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[121, 117])).
% 80.64/50.92 tff(123,plain,(
% 80.64/50.92 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 80.64/50.92 inference(skolemize,[status(sab)],[122])).
% 80.64/50.92 tff(124,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[123, 116])).
% 80.64/50.92 tff(125,plain,
% 80.64/50.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[124, 114])).
% 80.64/50.92 tff(126,plain,
% 80.64/50.92 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 80.64/50.92 inference(rewrite,[status(thm)],[])).
% 80.64/50.92 tff(127,plain,
% 80.64/50.92 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) <=> ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 80.64/50.92 inference(rewrite,[status(thm)],[])).
% 80.64/50.92 tff(128,plain,
% 80.64/50.92 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))))),
% 80.64/50.92 inference(monotonicity,[status(thm)],[127])).
% 80.64/50.92 tff(129,plain,
% 80.64/50.92 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 80.64/50.92 inference(transitivity,[status(thm)],[128, 126])).
% 80.64/50.92 tff(130,plain,
% 80.64/50.92 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 80.64/50.92 inference(quant_inst,[status(thm)],[])).
% 80.64/50.92 tff(131,plain,
% 80.64/50.92 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[130, 129])).
% 80.64/50.92 tff(132,plain,
% 80.64/50.92 ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[131, 125])).
% 80.64/50.92 tff(133,plain,
% 80.64/50.92 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[132, 109, 102, 100, 78, 76, 74])).
% 80.64/50.92 tff(134,plain,
% 80.64/50.92 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 80.64/50.92 inference(rewrite,[status(thm)],[])).
% 80.64/50.92 tff(135,plain,
% 80.64/50.92 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 80.64/50.92 inference(quant_inst,[status(thm)],[])).
% 80.64/50.92 tff(136,plain,
% 80.64/50.92 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))))),
% 80.64/50.92 inference(modus_ponens,[status(thm)],[135, 134])).
% 80.64/50.92 tff(137,plain,
% 80.64/50.92 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[136, 133, 22])).
% 80.64/50.92 tff(138,plain,
% 80.64/50.92 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_struct_0(B!1) = u1_struct_0(A!0))),
% 80.64/50.92 inference(tautology,[status(thm)],[])).
% 80.64/50.92 tff(139,plain,
% 80.64/50.92 (u1_struct_0(B!1) = u1_struct_0(A!0)),
% 80.64/50.92 inference(unit_resolution,[status(thm)],[138, 137])).
% 80.64/50.92 tff(140,plain,
% 80.64/50.92 (k1_zfmisc_1(u1_struct_0(B!1)) = k1_zfmisc_1(u1_struct_0(A!0))),
% 80.64/50.92 inference(monotonicity,[status(thm)],[139])).
% 80.64/50.92 tff(141,plain,
% 80.64/50.92 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 80.64/50.92 inference(monotonicity,[status(thm)],[140])).
% 80.64/50.92 tff(142,plain,
% 80.64/50.92 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 80.64/50.92 inference(symmetry,[status(thm)],[141])).
% 80.64/50.92 tff(143,plain,
% 80.64/50.92 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(144,plain,
% 80.64/50.92 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[143])).
% 80.64/50.92 tff(145,plain,
% 80.64/50.92 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(146,plain,
% 80.64/50.92 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[145])).
% 80.64/50.92 tff(147,plain,
% 80.64/50.92 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 80.64/50.92 inference(transitivity,[status(thm)],[146, 144])).
% 80.64/50.92 tff(148,plain,
% 80.64/50.92 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 80.64/50.92 inference(bind,[status(th)],[])).
% 80.64/50.92 tff(149,plain,
% 80.64/50.92 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 80.64/50.92 inference(quant_intro,[status(thm)],[148])).
% 80.64/50.92 tff(150,plain,
% 80.64/50.92 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 80.64/50.92 inference(rewrite,[status(thm)],[])).
% 80.64/50.92 tff(151,plain,
% 80.64/50.92 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(152,plain,
% 80.64/50.93 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[151])).
% 80.64/50.93 tff(153,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_filter_2')).
% 80.64/50.93 tff(154,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[153, 152])).
% 80.64/50.93 tff(155,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[154, 150])).
% 80.64/50.93 tff(156,plain,(
% 80.64/50.93 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 80.64/50.93 inference(skolemize,[status(sab)],[155])).
% 80.64/50.93 tff(157,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[156, 149])).
% 80.64/50.93 tff(158,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[157, 147])).
% 80.64/50.93 tff(159,plain,
% 80.64/50.93 (l3_lattices(A!0)),
% 80.64/50.93 inference(and_elim,[status(thm)],[20])).
% 80.64/50.93 tff(160,plain,
% 80.64/50.93 (v10_lattices(A!0)),
% 80.64/50.93 inference(and_elim,[status(thm)],[20])).
% 80.64/50.93 tff(161,plain,
% 80.64/50.93 (~v3_struct_0(A!0)),
% 80.64/50.93 inference(and_elim,[status(thm)],[20])).
% 80.64/50.93 tff(162,plain,
% 80.64/50.93 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(163,plain,
% 80.64/50.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 80.64/50.93 inference(quant_inst,[status(thm)],[])).
% 80.64/50.93 tff(164,plain,
% 80.64/50.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[163, 162])).
% 80.64/50.93 tff(165,plain,
% 80.64/50.93 (![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 80.64/50.93 inference(unit_resolution,[status(thm)],[164, 161, 160, 159, 158])).
% 80.64/50.93 tff(166,plain,
% 80.64/50.93 (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))),
% 80.64/50.93 inference(and_elim,[status(thm)],[20])).
% 80.64/50.93 tff(167,plain,
% 80.64/50.93 (m1_filter_2(C!2, A!0)),
% 80.64/50.93 inference(or_elim,[status(thm)],[166])).
% 80.64/50.93 tff(168,plain,
% 80.64/50.93 (((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))) <=> ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(169,plain,
% 80.64/50.93 ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 80.64/50.93 inference(quant_inst,[status(thm)],[])).
% 80.64/50.93 tff(170,plain,
% 80.64/50.93 ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[169, 168])).
% 80.64/50.93 tff(171,plain,
% 80.64/50.93 (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))),
% 80.64/50.93 inference(unit_resolution,[status(thm)],[170, 167, 165])).
% 80.64/50.93 tff(172,plain,
% 80.64/50.93 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | m2_lattice4(C!2, A!0)),
% 80.64/50.93 inference(tautology,[status(thm)],[])).
% 80.64/50.93 tff(173,plain,
% 80.64/50.93 (m2_lattice4(C!2, A!0)),
% 80.64/50.93 inference(unit_resolution,[status(thm)],[172, 171])).
% 80.64/50.93 tff(174,plain,
% 80.64/50.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(175,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[174])).
% 80.64/50.93 tff(176,plain,
% 80.64/50.93 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(177,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[176])).
% 80.64/50.93 tff(178,plain,
% 80.64/50.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(179,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[178])).
% 80.64/50.93 tff(180,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 80.64/50.93 inference(transitivity,[status(thm)],[179, 177])).
% 80.64/50.93 tff(181,plain,
% 80.64/50.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(182,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[181])).
% 80.64/50.93 tff(183,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(184,plain,
% 80.64/50.93 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(185,plain,
% 80.64/50.93 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[184])).
% 80.64/50.93 tff(186,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 80.64/50.93 tff(187,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[186, 185])).
% 80.64/50.93 tff(188,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[187, 183])).
% 80.64/50.93 tff(189,plain,(
% 80.64/50.93 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(skolemize,[status(sab)],[188])).
% 80.64/50.93 tff(190,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[189, 182])).
% 80.64/50.93 tff(191,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[190, 180])).
% 80.64/50.93 tff(192,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[191, 175])).
% 80.64/50.93 tff(193,plain,
% 80.64/50.93 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(194,plain,
% 80.64/50.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 80.64/50.93 inference(quant_inst,[status(thm)],[])).
% 80.64/50.93 tff(195,plain,
% 80.64/50.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[194, 193])).
% 80.64/50.93 tff(196,plain,
% 80.64/50.93 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 80.64/50.93 inference(unit_resolution,[status(thm)],[195, 161, 160, 159, 192])).
% 80.64/50.93 tff(197,plain,
% 80.64/50.93 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(198,plain,
% 80.64/50.93 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 80.64/50.93 inference(quant_inst,[status(thm)],[])).
% 80.64/50.93 tff(199,plain,
% 80.64/50.93 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[198, 197])).
% 80.64/50.93 tff(200,plain,
% 80.64/50.93 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 80.64/50.93 inference(unit_resolution,[status(thm)],[199, 196, 173])).
% 80.64/50.93 tff(201,plain,
% 80.64/50.93 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[200, 142])).
% 80.64/50.93 tff(202,plain,
% 80.64/50.93 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | (~v1_xboole_0(C!2))),
% 80.64/50.93 inference(tautology,[status(thm)],[])).
% 80.64/50.93 tff(203,plain,
% 80.64/50.93 (~v1_xboole_0(C!2)),
% 80.64/50.93 inference(unit_resolution,[status(thm)],[202, 171])).
% 80.64/50.93 tff(204,plain,
% 80.64/50.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(205,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[204])).
% 80.64/50.93 tff(206,plain,
% 80.64/50.93 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(207,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[206])).
% 80.64/50.93 tff(208,plain,
% 80.64/50.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(209,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[208])).
% 80.64/50.93 tff(210,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(transitivity,[status(thm)],[209, 207])).
% 80.64/50.93 tff(211,plain,
% 80.64/50.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite(((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))), trans(monotonicity(trans(monotonicity(rewrite((~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))) <=> (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))), ((m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))) <=> (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))), rewrite((m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))) <=> (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))), ((m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))) <=> (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))), ((m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))), rewrite((m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))) <=> (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))), ((m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))), ((((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) <=> (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))), rewrite((((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))), ((((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) <=> (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(212,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[211])).
% 80.64/50.93 tff(213,plain,
% 80.64/50.93 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | ((~(~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(214,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | ((~(~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[213])).
% 80.64/50.93 tff(215,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(216,plain,
% 80.64/50.93 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) <=> (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))))),
% 80.64/50.93 inference(bind,[status(th)],[])).
% 80.64/50.93 tff(217,plain,
% 80.64/50.93 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))),
% 80.64/50.93 inference(quant_intro,[status(thm)],[216])).
% 80.64/50.93 tff(218,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_filter_0')).
% 80.64/50.93 tff(219,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[218, 217])).
% 80.64/50.93 tff(220,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[219, 215])).
% 80.64/50.93 tff(221,plain,(
% 80.64/50.93 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | ((~(~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 80.64/50.93 inference(skolemize,[status(sab)],[220])).
% 80.64/50.93 tff(222,plain,
% 80.64/50.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) & (m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[221, 214])).
% 80.64/50.93 tff(223,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[222, 212])).
% 80.64/50.93 tff(224,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B)))))) | (~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[223, 210])).
% 80.64/50.93 tff(225,plain,
% 80.64/50.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))),
% 80.64/50.93 inference(modus_ponens,[status(thm)],[224, 205])).
% 80.64/50.93 tff(226,plain,
% 80.64/50.93 (v10_lattices(B!1)),
% 80.64/50.93 inference(and_elim,[status(thm)],[20])).
% 80.64/50.93 tff(227,plain,
% 80.64/50.93 (~v3_struct_0(B!1)),
% 80.64/50.93 inference(and_elim,[status(thm)],[20])).
% 80.64/50.93 tff(228,plain,
% 80.64/50.93 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))),
% 80.64/50.93 inference(rewrite,[status(thm)],[])).
% 80.64/50.93 tff(229,plain,
% 80.64/50.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))),
% 80.64/50.93 inference(quant_inst,[status(thm)],[])).
% 80.64/50.93 tff(230,plain,
% 80.64/50.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[229, 228])).
% 80.64/50.94 tff(231,plain,
% 80.64/50.94 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[230, 227, 226, 45, 225])).
% 80.64/50.94 tff(232,plain,
% 80.64/50.94 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(233,plain,
% 80.64/50.94 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))))),
% 80.64/50.94 inference(quant_inst,[status(thm)],[])).
% 80.64/50.94 tff(234,plain,
% 80.64/50.94 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B)))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[233, 232])).
% 80.64/50.94 tff(235,plain,
% 80.64/50.94 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[234, 231, 203])).
% 80.64/50.94 tff(236,plain,
% 80.64/50.94 (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[235, 201])).
% 80.64/50.94 tff(237,plain,
% 80.64/50.94 (((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))) | (m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))),
% 80.64/50.94 inference(tautology,[status(thm)],[])).
% 80.64/50.94 tff(238,plain,
% 80.64/50.94 (m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[237, 236])).
% 80.64/50.94 tff(239,plain,
% 80.64/50.94 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(240,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[239])).
% 80.64/50.94 tff(241,plain,
% 80.64/50.94 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(242,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[241])).
% 80.64/50.94 tff(243,plain,
% 80.64/50.94 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(244,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[243])).
% 80.64/50.94 tff(245,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 80.64/50.94 inference(transitivity,[status(thm)],[244, 242])).
% 80.64/50.94 tff(246,plain,
% 80.64/50.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(247,plain,
% 80.64/50.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[246])).
% 80.64/50.94 tff(248,plain,
% 80.64/50.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(249,plain,
% 80.64/50.94 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(250,plain,
% 80.64/50.94 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[249])).
% 80.64/50.94 tff(251,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 80.64/50.94 tff(252,plain,
% 80.64/50.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[251, 250])).
% 80.64/50.94 tff(253,plain,
% 80.64/50.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[252, 248])).
% 80.64/50.94 tff(254,plain,(
% 80.64/50.94 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(skolemize,[status(sab)],[253])).
% 80.64/50.94 tff(255,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[254, 247])).
% 80.64/50.94 tff(256,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[255, 245])).
% 80.64/50.94 tff(257,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[256, 240])).
% 80.64/50.94 tff(258,plain,
% 80.64/50.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(259,plain,
% 80.64/50.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 80.64/50.94 inference(quant_inst,[status(thm)],[])).
% 80.64/50.94 tff(260,plain,
% 80.64/50.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[259, 258])).
% 80.64/50.94 tff(261,plain,
% 80.64/50.94 (![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[260, 227, 226, 45, 257])).
% 80.64/50.94 tff(262,plain,
% 80.64/50.94 ((~![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))) | (m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))),
% 80.64/50.94 inference(quant_inst,[status(thm)],[])).
% 80.64/50.94 tff(263,plain,
% 80.64/50.94 (m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1)),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[262, 261])).
% 80.64/50.94 tff(264,plain,
% 80.64/50.94 (~m1_filter_2(C!2, B!1)),
% 80.64/50.94 inference(or_elim,[status(thm)],[166])).
% 80.64/50.94 tff(265,plain,
% 80.64/50.94 ((~(m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))) | m1_filter_2(C!2, B!1) | (~m1_filter_0(C!2, B!1))),
% 80.64/50.94 inference(tautology,[status(thm)],[])).
% 80.64/50.94 tff(266,plain,
% 80.64/50.94 ((~(m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))) | (~m1_filter_0(C!2, B!1))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[265, 264])).
% 80.64/50.94 tff(267,plain,
% 80.64/50.94 (~m1_filter_0(C!2, B!1)),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[266, 263])).
% 80.64/50.94 tff(268,plain,
% 80.64/50.94 ((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))),
% 80.64/50.94 inference(tautology,[status(thm)],[])).
% 80.64/50.94 tff(269,plain,
% 80.64/50.94 ((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[268, 267])).
% 80.64/50.94 tff(270,plain,
% 80.64/50.94 (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[269, 238])).
% 80.64/50.94 tff(271,plain,
% 80.64/50.94 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) | m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))),
% 80.64/50.94 inference(tautology,[status(thm)],[])).
% 80.64/50.94 tff(272,plain,
% 80.64/50.94 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[271, 270])).
% 80.64/50.94 tff(273,plain,
% 80.64/50.94 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) | m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))),
% 80.64/50.94 inference(tautology,[status(thm)],[])).
% 80.64/50.94 tff(274,plain,
% 80.64/50.94 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[273, 270])).
% 80.64/50.94 tff(275,plain,
% 80.64/50.94 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(276,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[275])).
% 80.64/50.94 tff(277,plain,
% 80.64/50.94 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(278,plain,
% 80.64/50.94 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[277])).
% 80.64/50.94 tff(279,plain,
% 80.64/50.94 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(280,plain,
% 80.64/50.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(281,plain,
% 80.64/50.94 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[280])).
% 80.64/50.94 tff(282,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_lattices')).
% 80.64/50.94 tff(283,plain,
% 80.64/50.94 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[282, 281])).
% 80.64/50.94 tff(284,plain,
% 80.64/50.94 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[283, 279])).
% 80.64/50.94 tff(285,plain,(
% 80.64/50.94 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 80.64/50.94 inference(skolemize,[status(sab)],[284])).
% 80.64/50.94 tff(286,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[285, 278])).
% 80.64/50.94 tff(287,plain,
% 80.64/50.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[286, 276])).
% 80.64/50.94 tff(288,plain,
% 80.64/50.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(289,plain,
% 80.64/50.94 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(290,plain,
% 80.64/50.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1))))))),
% 80.64/50.94 inference(monotonicity,[status(thm)],[289])).
% 80.64/50.94 tff(291,plain,
% 80.64/50.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))),
% 80.64/50.94 inference(transitivity,[status(thm)],[290, 288])).
% 80.64/50.94 tff(292,plain,
% 80.64/50.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1)))),
% 80.64/50.94 inference(quant_inst,[status(thm)],[])).
% 80.64/50.94 tff(293,plain,
% 80.64/50.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[292, 291])).
% 80.64/50.94 tff(294,plain,
% 80.64/50.94 (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[293, 227, 226, 45, 287])).
% 80.64/50.94 tff(295,plain,
% 80.64/50.94 ((v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1))) | v6_lattices(B!1)),
% 80.64/50.94 inference(tautology,[status(thm)],[])).
% 80.64/50.94 tff(296,plain,
% 80.64/50.94 (v6_lattices(B!1)),
% 80.64/50.94 inference(unit_resolution,[status(thm)],[295, 294])).
% 80.64/50.94 tff(297,plain,
% 80.64/50.94 (^[A: $i, B: $i, C: $i] : refl(((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(298,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[297])).
% 80.64/50.94 tff(299,plain,
% 80.64/50.94 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(300,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[299])).
% 80.64/50.94 tff(301,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(302,plain,
% 80.64/50.94 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))))),
% 80.64/50.94 inference(bind,[status(th)],[])).
% 80.64/50.94 tff(303,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 80.64/50.94 inference(quant_intro,[status(thm)],[302])).
% 80.64/50.94 tff(304,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 80.64/50.94 tff(305,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[304, 303])).
% 80.64/50.94 tff(306,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[305, 301])).
% 80.64/50.94 tff(307,plain,(
% 80.64/50.94 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 80.64/50.94 inference(skolemize,[status(sab)],[306])).
% 80.64/50.94 tff(308,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[307, 300])).
% 80.64/50.94 tff(309,plain,
% 80.64/50.94 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.94 inference(modus_ponens,[status(thm)],[308, 298])).
% 80.64/50.94 tff(310,plain,
% 80.64/50.94 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(311,plain,
% 80.64/50.94 (((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1)))) <=> (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.94 inference(rewrite,[status(thm)],[])).
% 80.64/50.94 tff(312,plain,
% 80.64/50.94 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))))),
% 80.64/50.94 inference(monotonicity,[status(thm)],[311])).
% 80.64/50.94 tff(313,plain,
% 80.64/50.94 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.95 inference(transitivity,[status(thm)],[312, 310])).
% 80.64/50.95 tff(314,plain,
% 80.64/50.95 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))),
% 80.64/50.95 inference(quant_inst,[status(thm)],[])).
% 80.64/50.95 tff(315,plain,
% 80.64/50.95 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[314, 313])).
% 80.64/50.95 tff(316,plain,
% 80.64/50.95 (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[315, 227, 309, 51, 296, 274, 272])).
% 80.64/50.95 tff(317,plain,
% 80.64/50.95 (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))),
% 80.64/50.95 inference(symmetry,[status(thm)],[316])).
% 80.64/50.95 tff(318,plain,
% 80.64/50.95 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(319,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[318])).
% 80.64/50.95 tff(320,plain,
% 80.64/50.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(321,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[320])).
% 80.64/50.95 tff(322,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(323,plain,
% 80.64/50.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(324,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[323])).
% 80.64/50.95 tff(325,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 80.64/50.95 tff(326,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[325, 324])).
% 80.64/50.95 tff(327,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[326, 322])).
% 80.64/50.95 tff(328,plain,(
% 80.64/50.95 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 80.64/50.95 inference(skolemize,[status(sab)],[327])).
% 80.64/50.95 tff(329,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[328, 321])).
% 80.64/50.95 tff(330,plain,
% 80.64/50.95 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[329, 319])).
% 80.64/50.95 tff(331,plain,
% 80.64/50.95 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(332,plain,
% 80.64/50.95 ((v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1)))) <=> (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(333,plain,
% 80.64/50.95 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))))),
% 80.64/50.95 inference(monotonicity,[status(thm)],[332])).
% 80.64/50.95 tff(334,plain,
% 80.64/50.95 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.95 inference(transitivity,[status(thm)],[333, 331])).
% 80.64/50.95 tff(335,plain,
% 80.64/50.95 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))))),
% 80.64/50.95 inference(quant_inst,[status(thm)],[])).
% 80.64/50.95 tff(336,plain,
% 80.64/50.95 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[335, 334])).
% 80.64/50.95 tff(337,plain,
% 80.64/50.95 (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[336, 227, 330, 51, 296, 274, 272])).
% 80.64/50.95 tff(338,plain,
% 80.64/50.95 (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.95 inference(symmetry,[status(thm)],[337])).
% 80.64/50.95 tff(339,plain,
% 80.64/50.95 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(340,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[339])).
% 80.64/50.95 tff(341,plain,
% 80.64/50.95 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(342,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[341])).
% 80.64/50.95 tff(343,plain,
% 80.64/50.95 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(344,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[343])).
% 80.64/50.95 tff(345,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 80.64/50.95 inference(transitivity,[status(thm)],[344, 342])).
% 80.64/50.95 tff(346,plain,
% 80.64/50.95 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(347,plain,
% 80.64/50.95 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[346])).
% 80.64/50.95 tff(348,plain,
% 80.64/50.95 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(349,plain,
% 80.64/50.95 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))))),
% 80.64/50.95 inference(bind,[status(th)],[])).
% 80.64/50.95 tff(350,plain,
% 80.64/50.95 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(quant_intro,[status(thm)],[349])).
% 80.64/50.95 tff(351,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattices')).
% 80.64/50.95 tff(352,plain,
% 80.64/50.95 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[351, 350])).
% 80.64/50.95 tff(353,plain,
% 80.64/50.95 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[352, 348])).
% 80.64/50.95 tff(354,plain,(
% 80.64/50.95 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(skolemize,[status(sab)],[353])).
% 80.64/50.95 tff(355,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[354, 347])).
% 80.64/50.95 tff(356,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[355, 345])).
% 80.64/50.95 tff(357,plain,
% 80.64/50.95 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[356, 340])).
% 80.64/50.95 tff(358,plain,
% 80.64/50.95 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C)))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(359,plain,
% 80.64/50.95 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C)))))),
% 80.64/50.95 inference(quant_inst,[status(thm)],[])).
% 80.64/50.95 tff(360,plain,
% 80.64/50.95 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[359, 358])).
% 80.64/50.95 tff(361,plain,
% 80.64/50.95 ((~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[360, 227, 357])).
% 80.64/50.95 tff(362,plain,
% 80.64/50.95 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[361, 51])).
% 80.64/50.95 tff(363,plain,
% 80.64/50.95 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(364,plain,
% 80.64/50.95 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C))))),
% 80.64/50.95 inference(quant_inst,[status(thm)],[])).
% 80.64/50.95 tff(365,plain,
% 80.64/50.95 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[364, 363])).
% 80.64/50.95 tff(366,plain,
% 80.64/50.95 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[365, 362, 272])).
% 80.64/50.95 tff(367,plain,
% 80.64/50.95 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(368,plain,
% 80.64/50.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.95 inference(quant_inst,[status(thm)],[])).
% 80.64/50.95 tff(369,plain,
% 80.64/50.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[368, 367])).
% 80.64/50.95 tff(370,plain,
% 80.64/50.95 (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[369, 274, 366])).
% 80.64/50.95 tff(371,plain,
% 80.64/50.95 (k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.95 inference(symmetry,[status(thm)],[370])).
% 80.64/50.95 tff(372,plain,
% 80.64/50.95 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_lattices(B!1) = u1_lattices(A!0))),
% 80.64/50.95 inference(tautology,[status(thm)],[])).
% 80.64/50.95 tff(373,plain,
% 80.64/50.95 (u1_lattices(B!1) = u1_lattices(A!0)),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[372, 137])).
% 80.64/50.95 tff(374,plain,
% 80.64/50.95 (u1_lattices(A!0) = u1_lattices(B!1)),
% 80.64/50.95 inference(symmetry,[status(thm)],[373])).
% 80.64/50.95 tff(375,plain,
% 80.64/50.95 (u1_struct_0(A!0) = u1_struct_0(B!1)),
% 80.64/50.95 inference(symmetry,[status(thm)],[139])).
% 80.64/50.95 tff(376,plain,
% 80.64/50.95 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.95 inference(monotonicity,[status(thm)],[375, 375, 375, 374])).
% 80.64/50.95 tff(377,plain,
% 80.64/50.95 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0)) <=> m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))),
% 80.64/50.95 inference(monotonicity,[status(thm)],[375])).
% 80.64/50.95 tff(378,plain,
% 80.64/50.95 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1)) <=> m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))),
% 80.64/50.95 inference(symmetry,[status(thm)],[377])).
% 80.64/50.95 tff(379,plain,
% 80.64/50.95 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[274, 378])).
% 80.64/50.95 tff(380,plain,
% 80.64/50.95 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0)) <=> m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))),
% 80.64/50.95 inference(monotonicity,[status(thm)],[375])).
% 80.64/50.95 tff(381,plain,
% 80.64/50.95 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1)) <=> m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))),
% 80.64/50.95 inference(symmetry,[status(thm)],[380])).
% 80.64/50.95 tff(382,plain,
% 80.64/50.95 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[272, 381])).
% 80.64/50.95 tff(383,plain,
% 80.64/50.95 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 80.64/50.95 inference(rewrite,[status(thm)],[])).
% 80.64/50.95 tff(384,plain,
% 80.64/50.95 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 80.64/50.95 inference(quant_inst,[status(thm)],[])).
% 80.64/50.95 tff(385,plain,
% 80.64/50.95 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 80.64/50.95 inference(modus_ponens,[status(thm)],[384, 383])).
% 80.64/50.95 tff(386,plain,
% 80.64/50.95 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 80.64/50.95 inference(unit_resolution,[status(thm)],[385, 159, 44])).
% 80.64/50.96 tff(387,plain,
% 80.64/50.96 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 80.64/50.96 inference(tautology,[status(thm)],[])).
% 80.64/50.96 tff(388,plain,
% 80.64/50.96 (l1_lattices(A!0)),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[387, 386])).
% 80.64/50.96 tff(389,plain,
% 80.64/50.96 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(390,plain,
% 80.64/50.96 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 80.64/50.96 inference(quant_inst,[status(thm)],[])).
% 80.64/50.96 tff(391,plain,
% 80.64/50.96 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[390, 389])).
% 80.64/50.96 tff(392,plain,
% 80.64/50.96 ((~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[391, 161, 357])).
% 80.64/50.96 tff(393,plain,
% 80.64/50.96 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[392, 388])).
% 80.64/50.96 tff(394,plain,
% 80.64/50.96 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(395,plain,
% 80.64/50.96 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C))))),
% 80.64/50.96 inference(quant_inst,[status(thm)],[])).
% 80.64/50.96 tff(396,plain,
% 80.64/50.96 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[395, 394])).
% 80.64/50.96 tff(397,plain,
% 80.64/50.96 ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[396, 393])).
% 80.64/50.96 tff(398,plain,
% 80.64/50.96 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[397, 382])).
% 80.64/50.96 tff(399,plain,
% 80.64/50.96 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(400,plain,
% 80.64/50.96 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.96 inference(quant_inst,[status(thm)],[])).
% 80.64/50.96 tff(401,plain,
% 80.64/50.96 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[400, 399])).
% 80.64/50.96 tff(402,plain,
% 80.64/50.96 (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[401, 398, 379])).
% 80.64/50.96 tff(403,plain,
% 80.64/50.96 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(404,plain,
% 80.64/50.96 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(405,plain,
% 80.64/50.96 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 80.64/50.96 inference(monotonicity,[status(thm)],[404])).
% 80.64/50.96 tff(406,plain,
% 80.64/50.96 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 80.64/50.96 inference(transitivity,[status(thm)],[405, 403])).
% 80.64/50.96 tff(407,plain,
% 80.64/50.96 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 80.64/50.96 inference(quant_inst,[status(thm)],[])).
% 80.64/50.96 tff(408,plain,
% 80.64/50.96 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[407, 406])).
% 80.64/50.96 tff(409,plain,
% 80.64/50.96 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[408, 161, 160, 159, 287])).
% 80.64/50.96 tff(410,plain,
% 80.64/50.96 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 80.64/50.96 inference(tautology,[status(thm)],[])).
% 80.64/50.96 tff(411,plain,
% 80.64/50.96 (v6_lattices(A!0)),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[410, 409])).
% 80.64/50.96 tff(412,plain,
% 80.64/50.96 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(413,plain,
% 80.64/50.96 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(414,plain,
% 80.64/50.96 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))))),
% 80.64/50.96 inference(monotonicity,[status(thm)],[413])).
% 80.64/50.96 tff(415,plain,
% 80.64/50.96 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 80.64/50.96 inference(transitivity,[status(thm)],[414, 412])).
% 80.64/50.96 tff(416,plain,
% 80.64/50.96 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))),
% 80.64/50.96 inference(quant_inst,[status(thm)],[])).
% 80.64/50.96 tff(417,plain,
% 80.64/50.96 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[416, 415])).
% 80.64/50.96 tff(418,plain,
% 80.64/50.96 (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[417, 161, 330, 388, 411, 382, 379])).
% 80.64/50.96 tff(419,plain,
% 80.64/50.96 (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))),
% 80.64/50.96 inference(transitivity,[status(thm)],[418, 402, 376, 371, 338, 317])).
% 80.64/50.96 tff(420,plain,
% 80.64/50.96 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 80.64/50.96 inference(monotonicity,[status(thm)],[419])).
% 80.64/50.96 tff(421,plain,
% 80.64/50.96 (r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.64/50.96 inference(symmetry,[status(thm)],[420])).
% 80.64/50.96 tff(422,plain,
% 80.64/50.96 ((~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) <=> (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 80.64/50.96 inference(monotonicity,[status(thm)],[421])).
% 80.64/50.96 tff(423,assumption,((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))), introduced(assumption)).
% 80.64/50.96 tff(424,plain,
% 80.64/50.96 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) | (~((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))),
% 80.64/50.96 inference(tautology,[status(thm)],[])).
% 80.64/50.96 tff(425,plain,
% 80.64/50.96 (~((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[424, 270])).
% 80.64/50.96 tff(426,plain,
% 80.64/50.96 (((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) | (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 80.64/50.96 inference(tautology,[status(thm)],[])).
% 80.64/50.96 tff(427,plain,
% 80.64/50.96 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[426, 425])).
% 80.64/50.96 tff(428,plain,
% 80.64/50.96 (r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[427, 423])).
% 80.64/50.96 tff(429,plain,
% 80.64/50.96 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[428, 421])).
% 80.64/50.96 tff(430,plain,
% 80.64/50.96 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B))))))))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(431,plain,
% 80.64/50.96 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B))))))))))),
% 80.64/50.96 inference(quant_inst,[status(thm)],[])).
% 80.64/50.96 tff(432,plain,
% 80.64/50.96 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B)))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) | (~((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A, C, D), B))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B)))))))))),
% 80.64/50.96 inference(modus_ponens,[status(thm)],[431, 430])).
% 80.64/50.96 tff(433,plain,
% 80.64/50.96 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B)))))))))),
% 80.64/50.96 inference(unit_resolution,[status(thm)],[432, 161, 160, 159, 225])).
% 80.64/50.96 tff(434,plain,
% 80.64/50.96 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B)))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B)))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))))),
% 80.64/50.96 inference(rewrite,[status(thm)],[])).
% 80.64/50.96 tff(435,plain,
% 80.64/50.96 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B)))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))))),
% 80.64/50.97 inference(quant_inst,[status(thm)],[])).
% 80.64/50.97 tff(436,plain,
% 80.64/50.97 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B)))))) | (~((~m1_filter_0(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, B)) | (~r2_hidden(D, B)))) <=> r2_hidden(k4_lattices(A!0, C, D), B)))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))))),
% 80.64/50.97 inference(modus_ponens,[status(thm)],[435, 434])).
% 80.64/50.97 tff(437,plain,
% 80.64/50.97 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[436, 433, 203])).
% 80.64/50.97 tff(438,plain,
% 80.64/50.97 (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[437, 200])).
% 80.64/50.97 tff(439,plain,
% 80.64/50.97 (((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2)))))) | (~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))) | ((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))),
% 80.64/50.97 inference(tautology,[status(thm)],[])).
% 80.64/50.97 tff(440,plain,
% 80.64/50.97 ((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[439, 438])).
% 80.64/50.97 tff(441,plain,
% 80.64/50.97 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 80.64/50.97 inference(rewrite,[status(thm)],[])).
% 80.64/50.97 tff(442,plain,
% 80.64/50.97 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 80.64/50.97 inference(quant_inst,[status(thm)],[])).
% 80.64/50.97 tff(443,plain,
% 80.64/50.97 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 80.64/50.97 inference(modus_ponens,[status(thm)],[442, 441])).
% 80.64/50.97 tff(444,plain,
% 80.64/50.97 (![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[443, 161, 160, 159, 257])).
% 80.64/50.97 tff(445,plain,
% 80.64/50.97 ((~![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))) | (m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))),
% 80.64/50.97 inference(quant_inst,[status(thm)],[])).
% 80.64/50.97 tff(446,plain,
% 80.64/50.97 (m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0)),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[445, 444])).
% 80.64/50.97 tff(447,plain,
% 80.64/50.97 ((~(m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))) | (~m1_filter_2(C!2, A!0)) | m1_filter_0(C!2, A!0)),
% 80.64/50.97 inference(tautology,[status(thm)],[])).
% 80.64/50.97 tff(448,plain,
% 80.64/50.97 ((~(m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))) | m1_filter_0(C!2, A!0)),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[447, 167])).
% 80.64/50.97 tff(449,plain,
% 80.64/50.97 (m1_filter_0(C!2, A!0)),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[448, 446])).
% 80.64/50.97 tff(450,plain,
% 80.64/50.97 ((~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))),
% 80.64/50.97 inference(tautology,[status(thm)],[])).
% 80.64/50.97 tff(451,plain,
% 80.64/50.97 ((~((~m1_filter_0(C!2, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[450, 449])).
% 80.64/50.97 tff(452,plain,
% 80.64/50.97 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[451, 440])).
% 80.64/50.97 tff(453,plain,
% 80.64/50.97 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 80.64/50.97 inference(rewrite,[status(thm)],[])).
% 80.64/50.97 tff(454,plain,
% 80.64/50.97 (((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))) <=> ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 80.64/50.97 inference(rewrite,[status(thm)],[])).
% 80.64/50.97 tff(455,plain,
% 80.64/50.97 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))),
% 80.64/50.97 inference(monotonicity,[status(thm)],[454])).
% 80.64/50.97 tff(456,plain,
% 80.64/50.97 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 80.64/50.97 inference(transitivity,[status(thm)],[455, 453])).
% 80.64/50.97 tff(457,plain,
% 80.64/50.97 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 80.64/50.97 inference(quant_inst,[status(thm)],[])).
% 80.64/50.97 tff(458,plain,
% 80.64/50.97 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2)))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))),
% 80.64/50.97 inference(modus_ponens,[status(thm)],[457, 456])).
% 80.64/50.97 tff(459,plain,
% 80.64/50.97 ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[458, 452])).
% 80.64/50.97 tff(460,plain,
% 80.64/50.97 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[459, 382])).
% 80.64/50.97 tff(461,plain,
% 80.64/50.97 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))),
% 80.64/50.97 inference(rewrite,[status(thm)],[])).
% 80.64/50.97 tff(462,plain,
% 80.64/50.97 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))),
% 80.64/50.97 inference(quant_inst,[status(thm)],[])).
% 80.64/50.97 tff(463,plain,
% 80.64/50.97 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((~((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 80.64/50.97 inference(modus_ponens,[status(thm)],[462, 461])).
% 80.64/50.97 tff(464,plain,
% 80.64/50.97 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[463, 460, 379])).
% 80.64/50.97 tff(465,plain,
% 80.64/50.97 ((~((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) | (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 80.64/50.97 inference(tautology,[status(thm)],[])).
% 80.64/50.97 tff(466,plain,
% 80.64/50.97 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[465, 464])).
% 80.64/50.97 tff(467,plain,
% 80.64/50.97 (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[466, 423])).
% 80.64/50.97 tff(468,plain,
% 80.64/50.97 ($false),
% 80.64/50.97 inference(unit_resolution,[status(thm)],[467, 429])).
% 80.64/50.97 tff(469,plain,(~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))), inference(lemma,lemma(discharge,[]))).
% 80.64/50.97 tff(470,plain,
% 80.64/50.97 (((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) | ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))),
% 80.64/50.97 inference(tautology,[status(thm)],[])).
% 80.64/50.97 tff(471,plain,
% 80.64/50.97 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))),
% 80.80/51.13 inference(unit_resolution,[status(thm)],[470, 425])).
% 80.80/51.13 tff(472,plain,
% 80.80/51.13 (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 80.80/51.13 inference(unit_resolution,[status(thm)],[471, 469])).
% 80.80/51.13 tff(473,plain,
% 80.80/51.13 (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.80/51.13 inference(modus_ponens,[status(thm)],[472, 422])).
% 80.80/51.13 tff(474,plain,
% 80.80/51.13 ((~((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) | ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.80/51.13 inference(tautology,[status(thm)],[])).
% 80.80/51.13 tff(475,plain,
% 80.80/51.13 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.80/51.13 inference(unit_resolution,[status(thm)],[474, 464])).
% 80.80/51.13 tff(476,plain,
% 80.80/51.13 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 80.80/51.13 inference(unit_resolution,[status(thm)],[475, 469])).
% 80.80/51.13 tff(477,plain,
% 80.80/51.13 ($false),
% 80.80/51.13 inference(unit_resolution,[status(thm)],[476, 473])).
% 80.80/51.13 % SZS output end Proof
%------------------------------------------------------------------------------