TSTP Solution File: LAT292+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT292+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 18:32:45 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT292+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Sep 1 13:18:16 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 % SZS output start Proof
% 0.18/0.47 tff(r1_filter_1_type, type, (
% 0.18/0.47 r1_filter_1: ( $i * $i ) > $o)).
% 0.18/0.47 tff(k6_lopclset_type, type, (
% 0.18/0.47 k6_lopclset: $i > $i)).
% 0.18/0.47 tff(k11_lopclset_type, type, (
% 0.18/0.47 k11_lopclset: $i > $i)).
% 0.18/0.47 tff(tptp_fun_A_0_type, type, (
% 0.18/0.47 tptp_fun_A_0: $i)).
% 0.18/0.47 tff(k12_lopclset_type, type, (
% 0.18/0.47 k12_lopclset: $i > $i)).
% 0.18/0.47 tff(v17_lattices_type, type, (
% 0.18/0.47 v17_lattices: $i > $o)).
% 0.18/0.47 tff(v10_lattices_type, type, (
% 0.18/0.47 v10_lattices: $i > $o)).
% 0.18/0.47 tff(l3_lattices_type, type, (
% 0.18/0.47 l3_lattices: $i > $o)).
% 0.18/0.47 tff(v3_struct_0_type, type, (
% 0.18/0.47 v3_struct_0: $i > $o)).
% 0.18/0.47 tff(v3_realset2_type, type, (
% 0.18/0.47 v3_realset2: $i > $o)).
% 0.18/0.47 tff(l1_pre_topc_type, type, (
% 0.18/0.47 l1_pre_topc: $i > $o)).
% 0.18/0.47 tff(v2_pre_topc_type, type, (
% 0.18/0.47 v2_pre_topc: $i > $o)).
% 0.18/0.47 tff(v1_pre_topc_type, type, (
% 0.18/0.47 v1_pre_topc: $i > $o)).
% 0.18/0.47 tff(1,plain,
% 0.18/0.47 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(2,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.47 tff(3,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(4,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.47 tff(5,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(6,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(7,plain,
% 0.18/0.47 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.47 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_lopclset')).
% 0.18/0.47 tff(9,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.47 tff(10,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.47 tff(11,plain,(
% 0.18/0.47 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[10])).
% 0.18/0.47 tff(12,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.18/0.47 tff(13,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.18/0.47 tff(14,plain,
% 0.18/0.47 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(15,plain,
% 0.18/0.47 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(16,plain,
% 0.18/0.47 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.47 tff(17,plain,
% 0.18/0.47 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.47 tff(18,plain,
% 0.18/0.47 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(19,plain,
% 0.18/0.47 ((~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ?[B: $i] : ((((~v3_struct_0(B)) & v2_pre_topc(B)) & l1_pre_topc(B)) & r1_filter_1(A, k6_lopclset(B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(20,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ?[B: $i] : ((((~v3_struct_0(B)) & v2_pre_topc(B)) & l1_pre_topc(B)) & r1_filter_1(A, k6_lopclset(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t44_lopclset')).
% 0.18/0.47 tff(21,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.47 tff(22,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.18/0.47 tff(23,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.47 tff(24,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.18/0.47 tff(25,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.18/0.47 tff(26,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.18/0.47 tff(27,plain,
% 0.18/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.18/0.47 tff(28,plain,
% 0.18/0.47 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.18/0.47 tff(29,plain,
% 0.18/0.47 (l3_lattices(A!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[28])).
% 0.18/0.47 tff(30,plain,
% 0.18/0.47 (~v3_realset2(A!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[28])).
% 0.18/0.47 tff(31,plain,
% 0.18/0.47 (v17_lattices(A!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[28])).
% 0.18/0.47 tff(32,plain,
% 0.18/0.47 (v10_lattices(A!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[28])).
% 0.18/0.47 tff(33,plain,
% 0.18/0.47 (~v3_struct_0(A!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[28])).
% 0.18/0.47 tff(34,plain,
% 0.18/0.47 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(35,plain,
% 0.18/0.47 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(36,plain,
% 0.18/0.47 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[35])).
% 0.18/0.47 tff(37,plain,
% 0.18/0.47 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[36, 34])).
% 0.18/0.47 tff(38,plain,
% 0.18/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(39,plain,
% 0.18/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.47 tff(40,plain,
% 0.18/0.47 (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[39, 33, 32, 31, 30, 29, 13])).
% 0.18/0.47 tff(41,plain,
% 0.18/0.47 (k6_lopclset(k11_lopclset(A!0)) = k12_lopclset(A!0)),
% 0.18/0.47 inference(symmetry,[status(thm)],[40])).
% 0.18/0.47 tff(42,plain,
% 0.18/0.47 (r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0))) <=> r1_filter_1(A!0, k12_lopclset(A!0))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.47 tff(43,plain,
% 0.18/0.47 (r1_filter_1(A!0, k12_lopclset(A!0)) <=> r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[42])).
% 0.18/0.47 tff(44,plain,
% 0.18/0.47 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(45,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.47 tff(46,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | r1_filter_1(A, k12_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(47,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.47 tff(48,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(50,plain,
% 0.18/0.47 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.47 tff(51,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_lopclset')).
% 0.18/0.47 tff(52,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.47 tff(54,plain,(
% 0.18/0.47 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[53])).
% 0.18/0.47 tff(55,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.18/0.47 tff(56,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.18/0.47 tff(57,plain,
% 0.18/0.47 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(58,plain,
% 0.18/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.47 tff(60,plain,
% 0.18/0.47 (r1_filter_1(A!0, k12_lopclset(A!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[59, 33, 32, 31, 30, 29, 56])).
% 0.18/0.47 tff(61,plain,
% 0.18/0.47 (r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[60, 43])).
% 0.18/0.47 tff(62,plain,
% 0.18/0.47 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(63,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.47 tff(64,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite(((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) <=> (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(65,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.47 tff(66,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(67,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A))) <=> ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(68,plain,
% 0.18/0.47 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.47 tff(69,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_lopclset')).
% 0.18/0.47 tff(70,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.47 tff(71,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.18/0.47 tff(72,plain,(
% 0.18/0.47 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[71])).
% 0.18/0.47 tff(73,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.18/0.47 tff(74,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.18/0.47 tff(75,plain,
% 0.18/0.47 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(76,plain,
% 0.18/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(77,plain,
% 0.18/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.47 tff(78,plain,
% 0.18/0.47 (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[77, 33, 32, 31, 30, 29, 74])).
% 0.18/0.47 tff(79,plain,
% 0.18/0.47 ((v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0)))) | (~v3_struct_0(k11_lopclset(A!0)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(80,plain,
% 0.18/0.47 (~v3_struct_0(k11_lopclset(A!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.18/0.47 tff(81,plain,
% 0.18/0.47 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(82,plain,
% 0.18/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))) <=> (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(84,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(86,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), rewrite(((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A))) <=> (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.47 tff(88,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k11_lopclset')).
% 0.18/0.48 tff(89,plain,
% 0.18/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.48 tff(90,plain,
% 0.18/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.48 tff(91,plain,(
% 0.18/0.48 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[90])).
% 0.18/0.48 tff(92,plain,
% 0.18/0.48 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.48 tff(93,plain,
% 0.18/0.48 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.18/0.48 tff(94,plain,
% 0.18/0.48 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(95,plain,
% 0.18/0.48 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(96,plain,
% 0.18/0.48 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.48 tff(97,plain,
% 0.18/0.48 (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[96, 33, 32, 31, 30, 29, 93])).
% 0.18/0.48 tff(98,plain,
% 0.18/0.48 (((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0)))) | l1_pre_topc(k11_lopclset(A!0))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(99,plain,
% 0.18/0.48 (l1_pre_topc(k11_lopclset(A!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.18/0.48 tff(100,plain,
% 0.18/0.48 (((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0)))) | v2_pre_topc(k11_lopclset(A!0))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(101,plain,
% 0.18/0.48 (v2_pre_topc(k11_lopclset(A!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.18/0.48 tff(102,plain,
% 0.18/0.48 (^[B: $i] : refl((v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))) <=> (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(103,plain,
% 0.18/0.48 (![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.48 tff(104,plain,
% 0.18/0.48 (^[B: $i] : trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))) <=> (~(v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))), ((~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))) <=> (~(~(v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))))), rewrite((~(~(v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))) <=> (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))), ((~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))) <=> (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(105,plain,
% 0.18/0.48 (![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.48 tff(106,plain,
% 0.18/0.48 (![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))),
% 0.18/0.48 inference(and_elim,[status(thm)],[28])).
% 0.18/0.48 tff(107,plain,
% 0.18/0.48 (![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.48 tff(108,plain,
% 0.18/0.48 (![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.18/0.48 tff(109,plain,
% 0.18/0.48 (((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | (v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(110,plain,
% 0.18/0.48 ((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | (v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(111,plain,
% 0.18/0.48 ((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.48 tff(112,plain,
% 0.18/0.48 (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[111, 108, 101, 99, 80])).
% 0.18/0.48 tff(113,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[112, 61])).
% 0.18/0.48 % SZS output end Proof
%------------------------------------------------------------------------------