%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP024+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:42:38 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : TOP024+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:53:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(u1_struct_0_type, type, (
% 0.20/0.43 u1_struct_0: $i > $i)).
% 0.20/0.43 tff(tptp_fun_A_0_type, type, (
% 0.20/0.43 tptp_fun_A_0: $i)).
% 0.20/0.43 tff(k6_pre_topc_type, type, (
% 0.20/0.43 k6_pre_topc: ( $i * $i ) > $i)).
% 0.20/0.43 tff(v1_tops_1_type, type, (
% 0.20/0.43 v1_tops_1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(m1_subset_1_type, type, (
% 0.20/0.43 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(k1_zfmisc_1_type, type, (
% 0.20/0.43 k1_zfmisc_1: $i > $i)).
% 0.20/0.43 tff(k2_pre_topc_type, type, (
% 0.20/0.43 k2_pre_topc: $i > $i)).
% 0.20/0.43 tff(l1_struct_0_type, type, (
% 0.20/0.43 l1_struct_0: $i > $o)).
% 0.20/0.43 tff(l1_pre_topc_type, type, (
% 0.20/0.43 l1_pre_topc: $i > $o)).
% 0.20/0.43 tff(tptp_fun_B_1_type, type, (
% 0.20/0.43 tptp_fun_B_1: $i)).
% 0.20/0.43 tff(v1_tsp_2_type, type, (
% 0.20/0.43 v1_tsp_2: ( $i * $i ) > $o)).
% 0.20/0.43 tff(v2_pre_topc_type, type, (
% 0.20/0.43 v2_pre_topc: $i > $o)).
% 0.20/0.43 tff(v3_struct_0_type, type, (
% 0.20/0.43 v3_struct_0: $i > $o)).
% 0.20/0.43 tff(k3_tex_4_type, type, (
% 0.20/0.43 k3_tex_4: ( $i * $i ) > $i)).
% 0.20/0.43 tff(v1_tsp_1_type, type, (
% 0.20/0.43 v1_tsp_1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.43 tff(6,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.43 tff(9,plain,(
% 0.20/0.43 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[8])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 ((((~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)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((~(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))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((((~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)))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 ((((~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)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ((~![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)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 ((~![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)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(17,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/sandbox/benchmark/theBenchmark.p','t2_tsp_2')).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (~![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (~![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (~![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (~![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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~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))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (l1_pre_topc(A!0)),
% 0.20/0.43 inference(and_elim,[status(thm)],[22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (l1_struct_0(A!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.43 tff(33,axiom,(![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_pre_topc')).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.44 tff(36,plain,(
% 0.20/0.44 ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[35])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 ((~![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (k2_pre_topc(A!0) = u1_struct_0(A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (u1_struct_0(A!0) = k2_pre_topc(A!0)),
% 0.20/0.44 inference(symmetry,[status(thm)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (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)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (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)))),
% 0.20/0.44 inference(symmetry,[status(thm)],[43])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.44 tff(50,axiom,(![A: $i] : (l1_struct_0(A) => m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_pre_topc')).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.44 tff(53,plain,(
% 0.20/0.44 ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (m1_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[57, 54, 27])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[58, 44])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (^[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)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.44 tff(68,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/sandbox/benchmark/theBenchmark.p','d2_tops_3')).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.44 tff(71,plain,(
% 0.20/0.44 ![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)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[70])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (((~![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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 ((~![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)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[75, 23, 72])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (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))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[79, 76, 59])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (v1_tops_1(u1_struct_0(A!0), A!0) <=> v1_tops_1(k2_pre_topc(A!0), A!0)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (v1_tops_1(k2_pre_topc(A!0), A!0) <=> v1_tops_1(u1_struct_0(A!0), A!0)),
% 0.20/0.44 inference(symmetry,[status(thm)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.44 tff(88,axiom,(![A: $i] : (l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc9_tops_1')).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.44 tff(91,plain,(
% 0.20/0.44 ![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.44 inference(skolemize,[status(sab)],[90])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (![A: $i] : ((~l1_pre_topc(A)) | v1_tops_1(k2_pre_topc(A), A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~![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))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~![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)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (v1_tops_1(k2_pre_topc(A!0), A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[95, 23, 92])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (v1_tops_1(u1_struct_0(A!0), A!0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[96, 82])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(106,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)))) | (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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.44 tff(107,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)))) | (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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(109,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))) => (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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.44 tff(110,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/sandbox/benchmark/theBenchmark.p','t64_tex_4')).
% 0.20/0.44 tff(111,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)))) | (k6_pre_topc(A, k3_tex_4(A, B)) = k6_pre_topc(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[110, 109])).
% 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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.45 tff(113,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)],[112])).
% 0.20/0.45 tff(114,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)],[113, 106])).
% 0.20/0.45 tff(115,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)],[114, 104])).
% 0.20/0.45 tff(116,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)],[115, 99])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (v2_pre_topc(A!0)),
% 0.20/0.45 inference(and_elim,[status(thm)],[22])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (~v3_struct_0(A!0)),
% 0.20/0.45 inference(and_elim,[status(thm)],[22])).
% 0.20/0.45 tff(119,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(120,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(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))))) | 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)],[120, 119])).
% 0.20/0.45 tff(122,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)],[121, 118, 117, 23, 116])).
% 0.20/0.45 tff(123,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)],[22])).
% 0.20/0.45 tff(124,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)],[123])).
% 0.20/0.45 tff(125,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(126,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(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)))) | (~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)],[126, 125])).
% 0.20/0.45 tff(128,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)],[127, 124, 122])).
% 0.20/0.45 tff(129,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(130,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.45 tff(131,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(132,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.45 tff(133,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.45 tff(134,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))))), 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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)) & 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.45 tff(136,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)))) | (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))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(137,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))) => (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))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(138,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))) => (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))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.45 tff(139,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/sandbox/benchmark/theBenchmark.p','d5_tsp_2')).
% 0.20/0.45 tff(140,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)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.45 tff(141,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)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.45 tff(142,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)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[141])).
% 0.20/0.45 tff(143,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.20/0.45 tff(144,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.20/0.45 tff(145,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, 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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(146,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(147,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_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, 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_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[147, 118, 117, 23, 144])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | ((~m1_subset_1(B!1, k1_zfmisc_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)))) <=> v1_tsp_2(B!1, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_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)))) <=> v1_tsp_2(B!1, A!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | ((~m1_subset_1(B!1, k1_zfmisc_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)))) <=> v1_tsp_2(B!1, A!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_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)))) <=> v1_tsp_2(B!1, A!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (~(((~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))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[151, 124, 148])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (v1_tsp_2(B!1, A!0)),
% 0.20/0.45 inference(or_elim,[status(thm)],[123])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 ((((~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))))) | (~v1_tsp_2(B!1, A!0))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ((((~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)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (((~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))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (k3_tex_4(A!0, B!1) = u1_struct_0(A!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (u1_struct_0(A!0) = k3_tex_4(A!0, B!1)),
% 0.20/0.45 inference(symmetry,[status(thm)],[158])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (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)],[159])).
% 0.20/0.46 tff(161,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)],[160, 128])).
% 0.20/0.46 tff(162,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)],[161])).
% 0.20/0.46 tff(163,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)],[162])).
% 0.20/0.46 tff(164,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)],[163])).
% 0.20/0.46 tff(165,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(166,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(167,plain,
% 0.20/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B, A!0) <=> (k6_pre_topc(A!0, B) = u1_struct_0(A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[167, 124, 76])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (~v1_tops_1(B!1, A!0)),
% 0.20/0.46 inference(or_elim,[status(thm)],[123])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 ((~(v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))) | v1_tops_1(B!1, A!0) | (~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 ((~(v1_tops_1(B!1, A!0) <=> (k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))) | (~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (~(k6_pre_topc(A!0, B!1) = u1_struct_0(A!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[171, 168])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (~(k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[172, 164])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 ((~(v1_tops_1(u1_struct_0(A!0), A!0) <=> (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0)))) | (~v1_tops_1(u1_struct_0(A!0), A!0)) | (k6_pre_topc(A!0, u1_struct_0(A!0)) = u1_struct_0(A!0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[174, 173, 97, 80])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------