TSTP Solution File: TOP024+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP024+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Fri Sep 30 01:55:52 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP024+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 09:51:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(u1_struct_0_type, type, (
% 0.20/0.44 u1_struct_0: $i > $i)).
% 0.20/0.44 tff(tptp_fun_A_0_type, type, (
% 0.20/0.44 tptp_fun_A_0: $i)).
% 0.20/0.44 tff(k6_pre_topc_type, type, (
% 0.20/0.44 k6_pre_topc: ( $i * $i ) > $i)).
% 0.20/0.44 tff(v1_tops_1_type, type, (
% 0.20/0.44 v1_tops_1: ( $i * $i ) > $o)).
% 0.20/0.44 tff(m1_subset_1_type, type, (
% 0.20/0.44 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.44 tff(k1_zfmisc_1_type, type, (
% 0.20/0.44 k1_zfmisc_1: $i > $i)).
% 0.20/0.44 tff(k2_pre_topc_type, type, (
% 0.20/0.44 k2_pre_topc: $i > $i)).
% 0.20/0.44 tff(l1_struct_0_type, type, (
% 0.20/0.44 l1_struct_0: $i > $o)).
% 0.20/0.44 tff(l1_pre_topc_type, type, (
% 0.20/0.44 l1_pre_topc: $i > $o)).
% 0.20/0.44 tff(tptp_fun_B_1_type, type, (
% 0.20/0.44 tptp_fun_B_1: $i)).
% 0.20/0.44 tff(v1_tsp_2_type, type, (
% 0.20/0.44 v1_tsp_2: ( $i * $i ) > $o)).
% 0.20/0.44 tff(v2_pre_topc_type, type, (
% 0.20/0.44 v2_pre_topc: $i > $o)).
% 0.20/0.44 tff(v3_struct_0_type, type, (
% 0.20/0.44 v3_struct_0: $i > $o)).
% 0.20/0.44 tff(k3_tex_4_type, type, (
% 0.20/0.44 k3_tex_4: ( $i * $i ) > $i)).
% 0.20/0.44 tff(v1_tsp_1_type, type, (
% 0.20/0.44 v1_tsp_1: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.44 tff(6,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.44 tff(9,plain,(
% 0.20/0.44 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[8])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 ((~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[13, 12])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[14, 11])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => v1_tops_1(B, A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(18,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => v1_tops_1(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_tsp_2')).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (v1_tops_1(B, A) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (l1_pre_topc(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[26])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (l1_struct_0(A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[30, 27, 10])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (^[A: $i] : refl(((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (^[A: $i] : rewrite((l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A))) <=> ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.45 tff(37,axiom,(![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_pre_topc')).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.45 tff(40,plain,(
% 0.20/0.45 ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[39])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | (~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | (~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (k2_pre_topc(A!0) = u1_struct_0(A!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (u1_struct_0(A!0) = k2_pre_topc(A!0)),
% 0.20/0.45 inference(symmetry,[status(thm)],[45])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(symmetry,[status(thm)],[47])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (^[A: $i] : refl(((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (^[A: $i] : rewrite((l1_struct_0(A) => m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) => m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.45 tff(54,axiom,(![A: $i] : (l1_struct_0(A) => m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_pre_topc')).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.45 tff(57,plain,(
% 0.20/0.45 ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[56])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | ((~l1_struct_0(A!0)) | m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | (~l1_struct_0(A!0)) | m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | ((~l1_struct_0(A!0)) | m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | (~l1_struct_0(A!0)) | m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[61, 58, 31])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 48])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.45 tff(72,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tops_3')).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.45 tff(75,plain,(
% 0.20/0.45 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[74])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tops_1(B, A) <=> (k6_pre_topc(A, B) = u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[79, 27, 76])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | ((~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | ((~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 ((~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[84, 63])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (v1_tops_1(u1_struct_0(A!0), A!0) <=> v1_tops_1(k2_pre_topc(A!0), A!0)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (v1_tops_1(k2_pre_topc(A!0), A!0) <=> v1_tops_1(u1_struct_0(A!0), A!0)),
% 0.20/0.45 inference(symmetry,[status(thm)],[86])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (^[A: $i] : refl(((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A)) <=> ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A)) <=> ![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A)) <=> ![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (^[A: $i] : rewrite((l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A), A)) <=> ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (![A: $i] : (l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A), A)) <=> ![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.45 tff(93,axiom,(![A: $i] : (l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc9_tops_1')).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.45 tff(96,plain,(
% 0.20/0.45 ![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(skolemize,[status(sab)],[95])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (((~![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))) | ((~l1_pre_topc(A!0)) | v1_tops_1(k2_pre_topc(A!0), A!0))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))) | (~l1_pre_topc(A!0)) | v1_tops_1(k2_pre_topc(A!0), A!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))) | ((~l1_pre_topc(A!0)) | v1_tops_1(k2_pre_topc(A!0), A!0))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 ((~![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))) | (~l1_pre_topc(A!0)) | v1_tops_1(k2_pre_topc(A!0), A!0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (v1_tops_1(k2_pre_topc(A!0), A!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[100, 27, 97])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (v1_tops_1(u1_struct_0(A!0), A!0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[101, 87])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.45 tff(115,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t64_tex_4')).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.45 tff(118,plain,(
% 0.20/0.45 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[117])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))) | (~v2_pre_topc(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 104])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (v2_pre_topc(A!0)),
% 0.20/0.45 inference(and_elim,[status(thm)],[26])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (~v3_struct_0(A!0)),
% 0.20/0.45 inference(and_elim,[status(thm)],[26])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 123, 122, 27, 121])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (~(v1_tops_1(B!1, A!0) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.45 inference(and_elim,[status(thm)],[26])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(or_elim,[status(thm)],[128])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B!1)) = k6_pre_topc(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B!1)) = k6_pre_topc(A!0, B!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B!1)) = k6_pre_topc(A!0, B!1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B)) = k6_pre_topc(A!0, B)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, k3_tex_4(A!0, B!1)) = k6_pre_topc(A!0, B!1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (k6_pre_topc(A!0, k3_tex_4(A!0, B!1)) = k6_pre_topc(A!0, B!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 129, 127])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.46 tff(144,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_tsp_2')).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.20/0.46 tff(147,plain,(
% 0.20/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[146])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[148, 138])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[152, 123, 122, 27, 149])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[156, 129, 153])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (v1_tsp_2(B!1, A!0)),
% 0.20/0.46 inference(or_elim,[status(thm)],[128])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ((~(v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))))) | (~v1_tsp_2(B!1, A!0)) | (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 ((~(v1_tsp_2(B!1, A!0) <=> (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))))) | (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[160, 157])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = u1_struct_0(A!0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (k3_tex_4(A!0, B!1) = u1_struct_0(A!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (u1_struct_0(A!0) = k3_tex_4(A!0, B!1)),
% 0.20/0.46 inference(symmetry,[status(thm)],[163])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (k6_pre_topc(A!0, u1_struct_0(A!0)) = k6_pre_topc(A!0, k3_tex_4(A!0, B!1))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (k6_pre_topc(A!0, u1_struct_0(A!0)) = k6_pre_topc(A!0, B!1)),
% 0.20/0.46 inference(transitivity,[status(thm)],[165, 133])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ((k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0)) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 ((k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[167])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 ((~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))) <=> (~(k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[168])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[172, 129, 80])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (~v1_tops_1(B!1, A!0)),
% 0.20/0.46 inference(or_elim,[status(thm)],[128])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ((~(v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))) | v1_tops_1(B!1, A!0) | (~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 ((~(v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))) | (~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[176, 173])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (~(k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[177, 169])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 ((~(v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0)))) | (~v1_tops_1(u1_struct_0(A!0), A!0)) | (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[179, 178, 102, 85])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------