%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP023+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:42:37 AM UTC 2025
% Result : Theorem 0.19s 0.50s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : TOP023+1 : TPTP v9.0.0. Released v3.4.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:51:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(m1_subset_1_type, type, (
% 0.19/0.50 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.50 tff(k1_zfmisc_1_type, type, (
% 0.19/0.50 k1_zfmisc_1: $i > $i)).
% 0.19/0.50 tff(u1_struct_0_type, type, (
% 0.19/0.50 u1_struct_0: $i > $i)).
% 0.19/0.50 tff(tptp_fun_A_0_type, type, (
% 0.19/0.50 tptp_fun_A_0: $i)).
% 0.19/0.50 tff(tptp_fun_C_3_type, type, (
% 0.19/0.50 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.19/0.50 tff(tptp_fun_B_1_type, type, (
% 0.19/0.50 tptp_fun_B_1: $i)).
% 0.19/0.50 tff(tptp_fun_C_2_type, type, (
% 0.19/0.50 tptp_fun_C_2: $i)).
% 0.19/0.50 tff(u1_pre_topc_type, type, (
% 0.19/0.50 u1_pre_topc: $i > $i)).
% 0.19/0.50 tff(g1_pre_topc_type, type, (
% 0.19/0.50 g1_pre_topc: ( $i * $i ) > $i)).
% 0.19/0.50 tff(v1_tsp_2_type, type, (
% 0.19/0.50 v1_tsp_2: ( $i * $i ) > $o)).
% 0.19/0.50 tff(l1_pre_topc_type, type, (
% 0.19/0.50 l1_pre_topc: $i > $o)).
% 0.19/0.50 tff(v1_tsp_1_type, type, (
% 0.19/0.50 v1_tsp_1: ( $i * $i ) > $o)).
% 0.19/0.50 tff(r1_tarski_type, type, (
% 0.19/0.50 r1_tarski: ( $i * $i ) > $o)).
% 0.19/0.50 tff(1,plain,
% 0.19/0.50 ((l1_pre_topc(A!0) & (l1_pre_topc(B!1) & (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)))))) <=> (l1_pre_topc(A!0) & l1_pre_topc(B!1) & (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 ((l1_pre_topc(B!1) & (~(v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1))))))) <=> (l1_pre_topc(B!1) & (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 ((l1_pre_topc(A!0) & (l1_pre_topc(B!1) & (~(v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))))))) <=> (l1_pre_topc(A!0) & (l1_pre_topc(B!1) & (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 ((l1_pre_topc(A!0) & (l1_pre_topc(B!1) & (~(v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))))))) <=> (l1_pre_topc(A!0) & l1_pre_topc(B!1) & (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[3, 1])).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))))) <=> (~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 ((~![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_2(C, A)) => v1_tsp_2(D, B))))))) <=> (~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(7,axiom,(~![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_2(C, A)) => v1_tsp_2(D, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_tsp_2')).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_2(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~v1_tsp_2(C, A)) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (l1_pre_topc(A!0) & l1_pre_topc(B!1) & (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (~((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | v1_tsp_2(C!2, B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_2(C!2, A!0)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[12])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1))),
% 0.19/0.50 inference(or_elim,[status(thm)],[13])).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0))),
% 0.19/0.50 inference(symmetry,[status(thm)],[14])).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (^[A: $i] : refl(((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (^[A: $i] : rewrite((l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (![A: $i] : (l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.50 tff(21,axiom,(![A: $i] : (l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_pre_topc')).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.50 tff(24,plain,(
% 0.19/0.50 ![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[23])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (l1_pre_topc(B!1)),
% 0.19/0.50 inference(and_elim,[status(thm)],[12])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (((~![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(B!1)) | m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(B!1)) | m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 ((~![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(B!1)) | m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 ((~![A: $i] : ((~l1_pre_topc(A)) | m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(B!1)) | m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[29, 26, 25])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (^[A: $i, B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(34,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.51 tff(35,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.51 tff(36,plain,
% 0.19/0.51 (^[A: $i, B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(37,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.51 tff(38,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(39,plain,
% 0.19/0.51 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((g1_pre_topc(A, B) = g1_pre_topc(C, D)) => ((A = C) & (B = D))) <=> ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((g1_pre_topc(A, B) = g1_pre_topc(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))), ((m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i, D: $i] : ((g1_pre_topc(A, B) = g1_pre_topc(C, D)) => ((A = C) & (B = D)))) <=> (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D)))))), rewrite((m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))), ((m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i, D: $i] : ((g1_pre_topc(A, B) = g1_pre_topc(C, D)) => ((A = C) & (B = D)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(40,plain,
% 0.19/0.51 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i, D: $i] : ((g1_pre_topc(A, B) = g1_pre_topc(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.51 tff(41,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => ![C: $i, D: $i] : ((g1_pre_topc(A, B) = g1_pre_topc(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g1_pre_topc')).
% 0.19/0.51 tff(42,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.51 tff(43,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.51 tff(44,plain,(
% 0.19/0.51 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | ((A = C) & (B = D))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[43])).
% 0.19/0.51 tff(45,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.51 tff(46,plain,
% 0.19/0.51 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1))))) | ![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D))))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1))))) | ![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(48,plain,
% 0.19/0.51 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1))))) | ![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(49,plain,
% 0.19/0.51 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) | ![C: $i, D: $i] : ((~(g1_pre_topc(A, B) = g1_pre_topc(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~m1_subset_1(u1_pre_topc(B!1), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B!1))))) | ![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 (![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[49, 46, 30])).
% 0.19/0.51 tff(51,plain,
% 0.19/0.51 (((~![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D)))))) | ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_pre_topc(B!1) = u1_pre_topc(A!0))))))) <=> ((~![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D)))))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_pre_topc(B!1) = u1_pre_topc(A!0))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 ((~![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D)))))) | ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_pre_topc(B!1) = u1_pre_topc(A!0))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 ((~![C: $i, D: $i] : ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(C, D))) | (~((~(u1_struct_0(B!1) = C)) | (~(u1_pre_topc(B!1) = D)))))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_pre_topc(B!1) = u1_pre_topc(A!0)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.51 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_pre_topc(B!1) = u1_pre_topc(A!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[53, 50, 15])).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_pre_topc(B!1) = u1_pre_topc(A!0)))) | (u1_struct_0(B!1) = u1_struct_0(A!0))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (u1_struct_0(B!1) = u1_struct_0(A!0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (k1_zfmisc_1(u1_struct_0(B!1)) = k1_zfmisc_1(u1_struct_0(A!0))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.51 tff(58,plain,
% 0.19/0.51 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(B!1))),
% 0.19/0.51 inference(symmetry,[status(thm)],[57])).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[59])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 (^[A: $i] : rewrite(((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, 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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(62,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (^[A: $i] : refl(((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, 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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(64,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 (^[A: $i] : rewrite(((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, 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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(66,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 (^[A: $i] : rewrite(((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, 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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 (![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, A)))))))))) <=> ![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 (^[A: $i] : rewrite(((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, 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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, A))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))))) <=> ![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))) <=> (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))), ((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) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> (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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))))))), rewrite((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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))))) <=> ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))), ((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) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (![A: $i] : (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) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> ![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.51 tff(75,axiom,(![A: $i] : (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) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tsp_2')).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.51 tff(78,plain,(
% 0.19/0.51 ![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[77])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (![A: $i] : ((~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) & ![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(C, A) & r1_tarski(B, C)))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(tptp_fun_C_3(B, A), A) & r1_tarski(B, tptp_fun_C_3(B, A))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A)))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[80, 67])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 (![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[81, 62])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1))))))))))))) <=> ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | (~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1))))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 (((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((B = tptp_fun_C_3(B, B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~r1_tarski(B, tptp_fun_C_3(B, B!1))))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (~r1_tarski(B, C)))))))))))) <=> ((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1))))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 (((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((B = tptp_fun_C_3(B, B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~r1_tarski(B, tptp_fun_C_3(B, B!1))))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (~r1_tarski(B, C))))))))))))) <=> ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.51 tff(86,plain,
% 0.19/0.51 (((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((B = tptp_fun_C_3(B, B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~r1_tarski(B, tptp_fun_C_3(B, B!1))))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (~r1_tarski(B, C))))))))))))) <=> ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | (~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1))))))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((B = tptp_fun_C_3(B, B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~r1_tarski(B, tptp_fun_C_3(B, B!1))))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (~r1_tarski(B, C))))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(88,plain,
% 0.19/0.52 ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | (~l1_pre_topc(B!1)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.52 tff(89,plain,
% 0.19/0.52 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[88, 26, 82])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.52 inference(or_elim,[status(thm)],[13])).
% 0.19/0.52 tff(91,plain,
% 0.19/0.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 (((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, B!1))))))))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, B!1)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C))))))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.52 tff(94,plain,
% 0.19/0.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, B!1)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.52 tff(95,plain,
% 0.19/0.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, B!1)))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(96,plain,
% 0.19/0.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(B, B!1) | (~v1_tsp_1(B, B!1)) | (~((~r1_tarski(B, tptp_fun_C_3(B, B!1))) | (~v1_tsp_1(tptp_fun_C_3(B, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(B, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (B = tptp_fun_C_3(B, B!1)))))) | (~((~v1_tsp_2(B, B!1)) | (~((~v1_tsp_1(B, B!1)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, B!1)))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.52 tff(97,plain,
% 0.19/0.52 (~((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[96, 90, 89])).
% 0.19/0.52 tff(98,plain,
% 0.19/0.52 (((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~((~v1_tsp_2(C!2, B!1)) | (~((~v1_tsp_1(C!2, B!1)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C, B!1)) | (C!2 = C) | (~r1_tarski(C!2, C))))))))) | (v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(99,plain,
% 0.19/0.52 (v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.52 tff(100,plain,
% 0.19/0.52 (l1_pre_topc(A!0)),
% 0.19/0.52 inference(and_elim,[status(thm)],[12])).
% 0.19/0.52 tff(101,plain,
% 0.19/0.52 (((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))) <=> ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | (~l1_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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(102,plain,
% 0.19/0.52 (((~l1_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)) | (~((B = tptp_fun_C_3(B, A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_3(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (~r1_tarski(B, C)))))))))))) <=> ((~l1_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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(103,plain,
% 0.19/0.52 (((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_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)) | (~((B = tptp_fun_C_3(B, A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_3(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (~r1_tarski(B, C))))))))))))) <=> ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.52 tff(104,plain,
% 0.19/0.52 (((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_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)) | (~((B = tptp_fun_C_3(B, A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_3(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (~r1_tarski(B, C))))))))))))) <=> ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | (~l1_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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.52 tff(105,plain,
% 0.19/0.52 ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | ((~l1_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)) | (~((B = tptp_fun_C_3(B, A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_3(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (~r1_tarski(B, C))))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(106,plain,
% 0.19/0.52 ((~![A: $i] : ((~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)) | (~((B = tptp_fun_C_3(B, A)) | (~m1_subset_1(tptp_fun_C_3(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_3(B, A), A)) | (~r1_tarski(B, tptp_fun_C_3(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(C, A)) | (~r1_tarski(B, C))))))))))))) | (~l1_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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.52 tff(107,plain,
% 0.19/0.52 (![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[106, 100, 82])).
% 0.19/0.52 tff(108,plain,
% 0.19/0.52 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.52 inference(or_elim,[status(thm)],[13])).
% 0.19/0.52 tff(109,plain,
% 0.19/0.52 (((~![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))) <=> ((~![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(110,plain,
% 0.19/0.53 (((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, A!0))))))))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(111,plain,
% 0.19/0.53 (((~![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, 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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.53 tff(112,plain,
% 0.19/0.53 (((~![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, 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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.53 tff(113,plain,
% 0.19/0.53 ((~![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((C!2 = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(C!2, C)) | (~v1_tsp_1(C, A!0)))))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(114,plain,
% 0.19/0.53 ((~![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)) | (~((~r1_tarski(B, tptp_fun_C_3(B, A!0))) | (~v1_tsp_1(tptp_fun_C_3(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_3(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.53 tff(115,plain,
% 0.19/0.53 (~((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[114, 108, 107])).
% 0.19/0.53 tff(116,plain,
% 0.19/0.53 (((~(v1_tsp_2(C!2, A!0) | (~v1_tsp_1(C!2, A!0)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, A!0))) | (~v1_tsp_1(tptp_fun_C_3(C!2, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (C!2 = tptp_fun_C_3(C!2, A!0)))))) | (~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))))))) | ((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(117,plain,
% 0.19/0.53 ((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.53 tff(118,plain,
% 0.19/0.53 (v1_tsp_2(C!2, A!0)),
% 0.19/0.53 inference(or_elim,[status(thm)],[13])).
% 0.19/0.53 tff(119,plain,
% 0.19/0.53 ((~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))) | (~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(120,plain,
% 0.19/0.53 ((~((~v1_tsp_2(C!2, A!0)) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))))) | (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.53 tff(121,plain,
% 0.19/0.53 (~((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.19/0.53 tff(122,plain,
% 0.19/0.53 (((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))) | v1_tsp_1(C!2, A!0)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(123,plain,
% 0.19/0.53 (v1_tsp_1(C!2, A!0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.53 tff(124,plain,
% 0.19/0.53 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(125,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.53 tff(126,plain,
% 0.19/0.53 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(127,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.53 tff(128,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.53 tff(129,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(130,plain,
% 0.19/0.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) <=> ((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))), (((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)) <=> (((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))), rewrite((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)) <=> ((~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))) | v1_tsp_1(D, B))), (((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)) <=> ((~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))) | v1_tsp_1(D, B)))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))) <=> (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))) | v1_tsp_1(D, B))))), rewrite((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))) | v1_tsp_1(D, B))) <=> (v1_tsp_1(D, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))) <=> (v1_tsp_1(D, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))) <=> ![D: $i] : (v1_tsp_1(D, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A)))))), trans(trans(der(![D: $i] : (v1_tsp_1(D, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A)))) <=> ![D: $i] : ((~v1_tsp_1(C, A)) | v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))), elim_unused(![D: $i] : ((~v1_tsp_1(C, A)) | v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))))) <=> ((~v1_tsp_1(C, A)) | v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))))), (![D: $i] : (v1_tsp_1(D, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A)))) <=> ((~v1_tsp_1(C, A)) | v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))))))), rewrite(((~v1_tsp_1(C, A)) | v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))))) <=> (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))), (![D: $i] : (v1_tsp_1(D, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) | (~((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D) & v1_tsp_1(C, A)))) <=> (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))) <=> (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))) <=> (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))) <=> (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))) <=> ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))), ((l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))))) <=> (l1_pre_topc(B) => ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))), rewrite((l1_pre_topc(B) => ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))) <=> ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))), ((l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))))) <=> ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))))), (![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))))) <=> ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))), ((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))), ((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(131,plain,
% 0.19/0.53 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B)))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.53 tff(132,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) => ((((g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B))) & (C = D)) & v1_tsp_1(C, A)) => v1_tsp_1(D, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_tsp_1')).
% 0.19/0.53 tff(133,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.53 tff(134,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.53 tff(135,plain,(
% 0.19/0.53 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(skolemize,[status(sab)],[134])).
% 0.19/0.53 tff(136,plain,
% 0.19/0.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.53 tff(137,plain,
% 0.19/0.53 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(138,plain,
% 0.19/0.53 (((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) <=> ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(139,plain,
% 0.19/0.53 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[138])).
% 0.19/0.53 tff(140,plain,
% 0.19/0.53 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[139, 137])).
% 0.19/0.54 tff(141,plain,
% 0.19/0.54 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0)))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(142,plain,
% 0.19/0.54 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.54 tff(143,plain,
% 0.19/0.54 (![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[142, 100, 136])).
% 0.19/0.54 tff(144,plain,
% 0.19/0.54 (((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | ((~l1_pre_topc(B!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1)))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | (~l1_pre_topc(B!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(145,plain,
% 0.19/0.54 (((~l1_pre_topc(B!1)) | ![C: $i] : (v1_tsp_1(C, B!1) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)))) <=> ((~l1_pre_topc(B!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(146,plain,
% 0.19/0.54 (((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | ((~l1_pre_topc(B!1)) | ![C: $i] : (v1_tsp_1(C, B!1) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | ((~l1_pre_topc(B!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.54 tff(147,plain,
% 0.19/0.54 (((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | ((~l1_pre_topc(B!1)) | ![C: $i] : (v1_tsp_1(C, B!1) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | (~l1_pre_topc(B!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.54 tff(148,plain,
% 0.19/0.54 ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | ((~l1_pre_topc(B!1)) | ![C: $i] : (v1_tsp_1(C, B!1) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(149,plain,
% 0.19/0.54 ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A!0))))) | (~l1_pre_topc(B!1)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.54 tff(150,plain,
% 0.19/0.54 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[149, 26, 143])).
% 0.19/0.54 tff(151,plain,
% 0.19/0.54 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | ((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(152,plain,
% 0.19/0.54 (((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1)) <=> ((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(153,plain,
% 0.19/0.54 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | ((~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1)))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[152])).
% 0.19/0.54 tff(154,plain,
% 0.19/0.54 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))),
% 0.19/0.54 inference(transitivity,[status(thm)],[153, 151])).
% 0.19/0.54 tff(155,plain,
% 0.19/0.54 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(156,plain,
% 0.19/0.54 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~v1_tsp_1(C, A!0)) | v1_tsp_1(C, B!1))) | (~(g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)) = g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(C!2, A!0)) | v1_tsp_1(C!2, B!1)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.54 tff(157,plain,
% 0.19/0.54 (v1_tsp_1(C!2, B!1)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[156, 14, 108, 90, 150, 123])).
% 0.19/0.54 tff(158,plain,
% 0.19/0.54 (~v1_tsp_2(C!2, B!1)),
% 0.19/0.54 inference(or_elim,[status(thm)],[13])).
% 0.19/0.54 tff(159,plain,
% 0.19/0.54 ((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(160,plain,
% 0.19/0.54 ((~(v1_tsp_2(C!2, B!1) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))))) | (~v1_tsp_1(C!2, B!1)) | (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.54 tff(161,plain,
% 0.19/0.54 (~((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[160, 157, 99])).
% 0.19/0.54 tff(162,plain,
% 0.19/0.54 (((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))) | m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(163,plain,
% 0.19/0.54 (m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.54 tff(164,plain,
% 0.19/0.54 (m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[163, 60])).
% 0.19/0.54 tff(165,plain,
% 0.19/0.54 (((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(166,plain,
% 0.19/0.54 (v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.19/0.54 tff(167,plain,
% 0.19/0.54 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | (~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(168,plain,
% 0.19/0.54 (((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) <=> ((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(169,plain,
% 0.19/0.54 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.54 tff(170,plain,
% 0.19/0.54 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | (~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.54 tff(171,plain,
% 0.19/0.54 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | ((~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1)))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(172,plain,
% 0.19/0.54 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, A)))))) | (~l1_pre_topc(B!1)) | ![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.54 tff(173,plain,
% 0.19/0.54 (![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[172, 26, 136])).
% 0.19/0.54 tff(174,plain,
% 0.19/0.54 (((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | ((~l1_pre_topc(A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0))))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | (~l1_pre_topc(A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(175,plain,
% 0.19/0.54 (((~l1_pre_topc(A!0)) | ![C: $i] : (v1_tsp_1(C, A!0) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~v1_tsp_1(C, B!1)))) <=> ((~l1_pre_topc(A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(176,plain,
% 0.19/0.54 (((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | ((~l1_pre_topc(A!0)) | ![C: $i] : (v1_tsp_1(C, A!0) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~v1_tsp_1(C, B!1))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | ((~l1_pre_topc(A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[175])).
% 0.19/0.55 tff(177,plain,
% 0.19/0.55 (((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | ((~l1_pre_topc(A!0)) | ![C: $i] : (v1_tsp_1(C, A!0) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~v1_tsp_1(C, B!1))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | (~l1_pre_topc(A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[176, 174])).
% 0.19/0.55 tff(178,plain,
% 0.19/0.55 ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | ((~l1_pre_topc(A!0)) | ![C: $i] : (v1_tsp_1(C, A!0) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~v1_tsp_1(C, B!1))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(179,plain,
% 0.19/0.55 ((~![B: $i] : ((~l1_pre_topc(B)) | ![C: $i] : (v1_tsp_1(C, B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(B), u1_pre_topc(B)))) | (~v1_tsp_1(C, B!1))))) | (~l1_pre_topc(A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.55 tff(180,plain,
% 0.19/0.55 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[179, 100, 173])).
% 0.19/0.55 tff(181,plain,
% 0.19/0.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(182,plain,
% 0.19/0.55 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0))))) <=> ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(183,plain,
% 0.19/0.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | ((~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.55 tff(184,plain,
% 0.19/0.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))),
% 0.19/0.55 inference(transitivity,[status(thm)],[183, 181])).
% 0.19/0.55 tff(185,plain,
% 0.19/0.55 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(186,plain,
% 0.19/0.55 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | v1_tsp_1(C, A!0) | (~v1_tsp_1(C, B!1)) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))))) | (~(g1_pre_topc(u1_struct_0(B!1), u1_pre_topc(B!1)) = g1_pre_topc(u1_struct_0(A!0), u1_pre_topc(A!0)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.55 tff(187,plain,
% 0.19/0.55 ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[186, 180, 166, 163, 15])).
% 0.19/0.55 tff(188,plain,
% 0.19/0.55 (v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[187, 164])).
% 0.19/0.55 tff(189,plain,
% 0.19/0.55 (((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))) | (~(C!2 = tptp_fun_C_3(C!2, B!1)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(190,plain,
% 0.19/0.55 (~(C!2 = tptp_fun_C_3(C!2, B!1))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[189, 161])).
% 0.19/0.55 tff(191,plain,
% 0.19/0.55 (((~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (C!2 = tptp_fun_C_3(C!2, B!1))) | r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(192,plain,
% 0.19/0.55 (r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[191, 161])).
% 0.19/0.55 tff(193,plain,
% 0.19/0.55 (((~v1_tsp_1(C!2, A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C))))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(194,plain,
% 0.19/0.55 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[193, 121])).
% 0.19/0.55 tff(195,plain,
% 0.19/0.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | ((C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(196,plain,
% 0.40/0.55 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1)))) <=> ((C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(197,plain,
% 0.40/0.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | ((C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[196])).
% 0.40/0.55 tff(198,plain,
% 0.40/0.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)))),
% 0.40/0.55 inference(transitivity,[status(thm)],[197, 195])).
% 0.40/0.55 tff(199,plain,
% 0.40/0.55 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0)) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(200,plain,
% 0.40/0.55 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (C!2 = C) | (~r1_tarski(C!2, C)))) | (C!2 = tptp_fun_C_3(C!2, B!1)) | (~r1_tarski(C!2, tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.40/0.55 tff(201,plain,
% 0.40/0.55 ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_3(C!2, B!1), A!0))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[200, 194, 192, 190])).
% 0.40/0.55 tff(202,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[201, 188, 164])).
% 0.40/0.55 % SZS output end Proof
% 0.40/0.56 % E exiting
%------------------------------------------------------------------------------