TSTP Solution File: LAT313+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT313+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 18:32:59 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : LAT313+1 : TPTP v8.1.0. Released v3.4.0.
% 0.04/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 14:17:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(r1_filter_2_type, type, (
% 0.19/0.44 r1_filter_2: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(k17_filter_2_type, type, (
% 0.19/0.44 k17_filter_2: $i > $i)).
% 0.19/0.44 tff(tptp_fun_A_0_type, type, (
% 0.19/0.44 tptp_fun_A_0: $i)).
% 0.19/0.44 tff(tptp_fun_B_1_type, type, (
% 0.19/0.44 tptp_fun_B_1: $i)).
% 0.19/0.44 tff(u1_struct_0_type, type, (
% 0.19/0.44 u1_struct_0: $i > $i)).
% 0.19/0.44 tff(k19_filter_2_type, type, (
% 0.19/0.44 k19_filter_2: ( $i * $i ) > $i)).
% 0.19/0.44 tff(v10_lattices_type, type, (
% 0.19/0.44 v10_lattices: $i > $o)).
% 0.19/0.44 tff(l3_lattices_type, type, (
% 0.19/0.44 l3_lattices: $i > $o)).
% 0.19/0.44 tff(v3_struct_0_type, type, (
% 0.19/0.44 v3_struct_0: $i > $o)).
% 0.19/0.44 tff(m2_filter_2_type, type, (
% 0.19/0.44 m2_filter_2: ( $i * $i ) > $o)).
% 0.19/0.44 tff(r2_hidden_type, type, (
% 0.19/0.44 r2_hidden: ( $i * $i ) > $o)).
% 0.19/0.44 tff(k6_lattices_type, type, (
% 0.19/0.44 k6_lattices: $i > $i)).
% 0.19/0.44 tff(v14_lattices_type, type, (
% 0.19/0.44 v14_lattices: $i > $o)).
% 0.19/0.44 tff(m1_subset_1_type, type, (
% 0.19/0.44 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.44 tff(k1_zfmisc_1_type, type, (
% 0.19/0.44 k1_zfmisc_1: $i > $i)).
% 0.19/0.44 tff(m2_lattice4_type, type, (
% 0.19/0.44 m2_lattice4: ( $i * $i ) > $o)).
% 0.19/0.44 tff(v1_xboole_0_type, type, (
% 0.19/0.44 v1_xboole_0: $i > $o)).
% 0.19/0.44 tff(l1_struct_0_type, type, (
% 0.19/0.44 l1_struct_0: $i > $o)).
% 0.19/0.44 tff(l2_lattices_type, type, (
% 0.19/0.44 l2_lattices: $i > $o)).
% 0.19/0.44 tff(l1_lattices_type, type, (
% 0.19/0.44 l1_lattices: $i > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[A: $i] : refl((v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (^[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))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (^[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)) => (k17_filter_2(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.45 tff(8,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_filter_2')).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.45 tff(11,plain,(
% 0.19/0.45 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[10])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 ((~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))) <=> (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 ((~(~((~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))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[16, 15])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[17, 14])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(21,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_filter_2')).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (l3_lattices(A!0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[29])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (v10_lattices(A!0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[29])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (~v3_struct_0(A!0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[29])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 ((v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (k17_filter_2(A!0) = u1_struct_0(A!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[38, 32, 31, 30, 13])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (u1_struct_0(A!0) = k17_filter_2(A!0)),
% 0.19/0.45 inference(symmetry,[status(thm)],[39])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (^[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(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (^[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_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_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] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.45 tff(51,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.45 tff(54,plain,(
% 0.19/0.45 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[53])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_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] : ((~m2_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] : ((~m2_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] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_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] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[59, 32, 31, 30, 56])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[29])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (m2_filter_2(B!1, A!0)),
% 0.19/0.45 inference(or_elim,[status(thm)],[61])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[65, 62, 60])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (m2_lattice4(B!1, A!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (^[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))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (^[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)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.45 tff(81,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')).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.46 tff(84,plain,(
% 0.19/0.46 ![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)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[83])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[86, 70])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (((~![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)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 ((~![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)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 32, 31, 30, 87])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, 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(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[94, 91, 68])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (^[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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (^[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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (^[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(rewrite((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) <=> (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A)))))), trans(monotonicity(rewrite((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) <=> (~((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) <=> (~(~((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))))), rewrite((~(~((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))) <=> ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))), ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) <=> ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), 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))))))), (((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))) | (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite(((~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))) | (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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))), (((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))), (![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & 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] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (^[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(((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))) <=> ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~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)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), (((((~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)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), (((((~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)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (![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)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.46 tff(106,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)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t42_filter_2')).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.19/0.46 tff(109,plain,(
% 0.19/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[108])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 (![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (((~![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), 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)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), 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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), 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)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 ((~![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), 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)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 ((~![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)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), 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)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[114, 32, 31, 30, 111])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 (^[A: $i, B: $i] : refl(((~v1_xboole_0(B)) | (~r2_hidden(A, B))) <=> ((~v1_xboole_0(B)) | (~r2_hidden(A, B))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (^[A: $i, B: $i] : trans(monotonicity(rewrite((r2_hidden(A, B) & v1_xboole_0(B)) <=> (~((~v1_xboole_0(B)) | (~r2_hidden(A, B))))), ((~(r2_hidden(A, B) & v1_xboole_0(B))) <=> (~(~((~v1_xboole_0(B)) | (~r2_hidden(A, B))))))), rewrite((~(~((~v1_xboole_0(B)) | (~r2_hidden(A, B))))) <=> ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))), ((~(r2_hidden(A, B) & v1_xboole_0(B))) <=> ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 (![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(121,axiom,(![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 (![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.46 tff(123,plain,(
% 0.19/0.46 ![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[122])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1)),
% 0.19/0.46 inference(or_elim,[status(thm)],[61])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (r2_hidden(k6_lattices(A!0), B!1)),
% 0.19/0.46 inference(and_elim,[status(thm)],[126])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1)))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | (~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | (~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (~v1_xboole_0(B!1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[130, 127, 125])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 (v14_lattices(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[126])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1))) <=> (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 ((~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) <=> (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1))) <=> (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[136, 134])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[138, 133])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[141, 132, 127, 131, 115])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[142, 95])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))) | (k19_filter_2(A!0, B!1) = u1_struct_0(A!0))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 (k19_filter_2(A!0, B!1) = u1_struct_0(A!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (k19_filter_2(A!0, B!1) = k17_filter_2(A!0)),
% 0.19/0.47 inference(transitivity,[status(thm)],[145, 40])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) <=> r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.47 inference(symmetry,[status(thm)],[148])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 (m2_filter_2(u1_struct_0(A!0), A!0) <=> m2_filter_2(k17_filter_2(A!0), A!0)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (m2_filter_2(k17_filter_2(A!0), A!0) <=> m2_filter_2(u1_struct_0(A!0), A!0)),
% 0.19/0.47 inference(symmetry,[status(thm)],[150])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (^[A: $i] : refl((m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (^[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))) | m2_filter_2(k17_filter_2(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m2_filter_2(k17_filter_2(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> ![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (^[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)) => m2_filter_2(k17_filter_2(A), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.47 tff(159,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k17_filter_2')).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.19/0.47 tff(162,plain,(
% 0.19/0.47 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.19/0.47 inference(skolemize,[status(sab)],[161])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 (![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[163, 153])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))) <=> ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 ((m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[166])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 (((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))),
% 0.19/0.47 inference(transitivity,[status(thm)],[167, 165])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (m2_filter_2(k17_filter_2(A!0), A!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[170, 32, 31, 30, 164])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 (m2_filter_2(u1_struct_0(A!0), A!0)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[171, 151])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 ((~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[175, 60])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[176, 172])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 ((v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))) | m2_lattice4(u1_struct_0(A!0), A!0)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (m2_lattice4(u1_struct_0(A!0), A!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), 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(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[182, 91, 179])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[183, 149])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[189])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[190, 188])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (^[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_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[192])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (^[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_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) <=> ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), (![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) <=> ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[195])).
% 0.19/0.47 tff(197,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t38_filter_2')).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.19/0.47 tff(200,plain,(
% 0.19/0.47 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[199])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[201, 191])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[202, 186])).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[206, 32, 31, 30, 203])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | ((~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | (~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | ((~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | (~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[210, 62, 207])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[212])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[214])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[217])).
% 0.19/0.47 tff(219,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.19/0.47 tff(222,plain,(
% 0.19/0.47 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[221])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[223, 213])).
% 0.19/0.47 tff(225,plain,
% 0.19/0.47 (((~![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)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.47 tff(228,plain,
% 0.19/0.47 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[227, 30, 224])).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (l2_lattices(A!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.47 tff(231,plain,
% 0.19/0.47 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(232,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[231])).
% 0.19/0.47 tff(233,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(234,plain,
% 0.19/0.47 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(235,plain,
% 0.19/0.47 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[234])).
% 0.19/0.47 tff(236,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.19/0.47 tff(237,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.19/0.47 tff(238,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.19/0.47 tff(239,plain,(
% 0.19/0.47 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[238])).
% 0.19/0.47 tff(240,plain,
% 0.19/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.19/0.47 tff(241,plain,
% 0.19/0.47 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(242,plain,
% 0.19/0.47 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(243,plain,
% 0.19/0.47 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.47 tff(244,plain,
% 0.19/0.47 (l1_struct_0(A!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[243, 240, 230])).
% 0.19/0.47 tff(245,plain,
% 0.19/0.47 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(246,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[245])).
% 0.19/0.47 tff(247,plain,
% 0.19/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(248,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[247])).
% 0.19/0.47 tff(249,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(250,plain,
% 0.19/0.47 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(251,plain,
% 0.19/0.47 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[250])).
% 0.19/0.47 tff(252,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.19/0.47 tff(253,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.19/0.47 tff(254,plain,
% 0.19/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.19/0.47 tff(255,plain,(
% 0.19/0.47 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[254])).
% 0.19/0.47 tff(256,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.19/0.47 tff(257,plain,
% 0.19/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[256, 246])).
% 0.19/0.47 tff(258,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(259,plain,
% 0.19/0.47 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(260,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[259])).
% 0.19/0.47 tff(261,plain,
% 0.19/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[260, 258])).
% 0.19/0.47 tff(262,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(263,plain,
% 0.19/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.47 tff(264,plain,
% 0.19/0.47 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[263, 32, 257])).
% 0.19/0.47 tff(265,plain,
% 0.19/0.47 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[264, 244])).
% 0.19/0.47 tff(266,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(267,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[266])).
% 0.19/0.47 tff(268,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))))), rewrite((r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(269,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[268])).
% 0.19/0.47 tff(270,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(271,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), rewrite((r1_filter_2(A, B, C) => r1_filter_2(A, C, B)) <=> ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(272,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[271])).
% 0.19/0.48 tff(273,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_filter_2')).
% 0.19/0.48 tff(274,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.48 tff(275,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.19/0.48 tff(276,plain,(
% 0.19/0.48 ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[275])).
% 0.19/0.48 tff(277,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.19/0.48 tff(278,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[277, 267])).
% 0.19/0.48 tff(279,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(280,plain,
% 0.19/0.48 ((v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(281,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[280])).
% 0.19/0.48 tff(282,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[281, 279])).
% 0.19/0.48 tff(283,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(284,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.19/0.48 tff(285,plain,
% 0.19/0.48 (r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[284, 278, 265, 95, 211])).
% 0.19/0.48 tff(286,plain,
% 0.19/0.48 (r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[285, 184])).
% 0.19/0.48 tff(287,plain,
% 0.19/0.48 (r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[286, 147])).
% 0.19/0.48 tff(288,plain,
% 0.19/0.48 ((u1_struct_0(A!0) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(289,plain,
% 0.19/0.48 ((k19_filter_2(A!0, B!1) = B!1) <=> (u1_struct_0(A!0) = B!1)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.48 tff(290,plain,
% 0.19/0.48 ((k19_filter_2(A!0, B!1) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.19/0.48 inference(transitivity,[status(thm)],[289, 288])).
% 0.19/0.48 tff(291,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : refl(((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(292,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[291])).
% 0.19/0.48 tff(293,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(294,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[293])).
% 0.19/0.48 tff(295,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(296,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(297,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[296])).
% 0.19/0.48 tff(298,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_filter_2')).
% 0.19/0.48 tff(299,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.19/0.48 tff(300,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.19/0.48 tff(301,plain,(
% 0.19/0.48 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[300])).
% 0.19/0.48 tff(302,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[301, 294])).
% 0.19/0.48 tff(303,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[302, 292])).
% 0.19/0.48 tff(304,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))) <=> ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(305,plain,
% 0.19/0.48 (((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(306,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[305])).
% 0.19/0.48 tff(307,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[306, 304])).
% 0.19/0.48 tff(308,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(309,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.48 tff(310,plain,
% 0.19/0.48 ((~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[309, 303, 265, 95])).
% 0.19/0.48 tff(311,plain,
% 0.19/0.48 (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[310, 184])).
% 0.19/0.48 tff(312,plain,
% 0.19/0.48 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (k19_filter_2(A!0, B!1) = B!1)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(313,plain,
% 0.19/0.48 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))) | (k19_filter_2(A!0, B!1) = B!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[312, 211])).
% 0.19/0.48 tff(314,plain,
% 0.19/0.48 (k19_filter_2(A!0, B!1) = B!1),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[313, 311])).
% 0.19/0.48 tff(315,plain,
% 0.19/0.48 (B!1 = u1_struct_0(A!0)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[314, 290])).
% 0.19/0.48 tff(316,plain,
% 0.19/0.48 ((~(~((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0)))))) <=> ((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(317,plain,
% 0.19/0.48 ((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) <=> (~((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(318,plain,
% 0.19/0.48 ((~(r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0)))) <=> (~(~((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[317])).
% 0.19/0.48 tff(319,plain,
% 0.19/0.48 ((~(r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0)))) <=> ((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[318, 316])).
% 0.19/0.48 tff(320,plain,
% 0.19/0.48 (~(r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0)))),
% 0.19/0.48 inference(or_elim,[status(thm)],[61])).
% 0.19/0.48 tff(321,plain,
% 0.19/0.48 ((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.19/0.48 tff(322,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[321, 315, 287])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------