%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP027+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:39 AM UTC 2025
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP027+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n013.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 13:52:38 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % SZS output start Proof
% 0.18/0.43 tff(k3_tex_4_type, type, (
% 0.18/0.43 k3_tex_4: ( $i * $i ) > $i)).
% 0.18/0.43 tff(k5_subset_1_type, type, (
% 0.18/0.43 k5_subset_1: ( $i * $i * $i ) > $i)).
% 0.18/0.43 tff(tptp_fun_B_1_type, type, (
% 0.18/0.43 tptp_fun_B_1: $i)).
% 0.18/0.43 tff(u1_struct_0_type, type, (
% 0.18/0.43 u1_struct_0: $i > $i)).
% 0.18/0.43 tff(tptp_fun_A_0_type, type, (
% 0.18/0.43 tptp_fun_A_0: $i)).
% 0.18/0.43 tff(v3_pre_topc_type, type, (
% 0.18/0.43 v3_pre_topc: ( $i * $i ) > $o)).
% 0.18/0.43 tff(m1_subset_1_type, type, (
% 0.18/0.43 m1_subset_1: ( $i * $i ) > $o)).
% 0.18/0.43 tff(k1_zfmisc_1_type, type, (
% 0.18/0.43 k1_zfmisc_1: $i > $i)).
% 0.18/0.43 tff(v1_tsp_2_type, type, (
% 0.18/0.43 v1_tsp_2: ( $i * $i ) > $o)).
% 0.18/0.43 tff(v2_pre_topc_type, type, (
% 0.18/0.43 v2_pre_topc: $i > $o)).
% 0.18/0.43 tff(l1_pre_topc_type, type, (
% 0.18/0.43 l1_pre_topc: $i > $o)).
% 0.18/0.43 tff(v3_struct_0_type, type, (
% 0.18/0.43 v3_struct_0: $i > $o)).
% 0.18/0.43 tff(k1_tops_1_type, type, (
% 0.18/0.43 k1_tops_1: ( $i * $i ) > $i)).
% 0.18/0.43 tff(tptp_fun_C_2_type, type, (
% 0.18/0.43 tptp_fun_C_2: $i)).
% 0.18/0.43 tff(1,plain,
% 0.18/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(2,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.43 tff(3,plain,
% 0.18/0.43 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(4,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.43 tff(5,plain,
% 0.18/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(6,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[5])).
% 0.18/0.43 tff(7,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[6, 4])).
% 0.18/0.43 tff(8,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(9,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.18/0.43 tff(10,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(11,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))) <=> ((~v3_pre_topc(C, A)) | (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_pre_topc(C, A)) | (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_pre_topc(C, A)) | (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))), ((v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))) <=> (v1_tsp_2(B, A) => ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))), rewrite((v1_tsp_2(B, A) => ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) <=> ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))), ((v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))) <=> ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))) <=> ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))) <=> ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(12,plain,
% 0.18/0.44 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.44 tff(13,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_tsp_2')).
% 0.18/0.44 tff(14,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.44 tff(15,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.44 tff(16,plain,(
% 0.18/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[15])).
% 0.18/0.44 tff(17,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.18/0.44 tff(18,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.18/0.44 tff(19,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.18/0.44 tff(20,plain,
% 0.18/0.44 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(21,plain,
% 0.18/0.44 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(22,plain,
% 0.18/0.44 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(23,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_tsp_2')).
% 0.18/0.44 tff(24,plain,
% 0.18/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.44 tff(25,plain,
% 0.18/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.18/0.44 tff(26,plain,
% 0.18/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.44 tff(27,plain,
% 0.18/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k1_tops_1(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k1_tops_1(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.18/0.44 tff(28,plain,
% 0.18/0.44 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 (l1_pre_topc(A!0)),
% 0.18/0.44 inference(and_elim,[status(thm)],[28])).
% 0.18/0.44 tff(30,plain,
% 0.18/0.44 (v2_pre_topc(A!0)),
% 0.18/0.44 inference(and_elim,[status(thm)],[28])).
% 0.18/0.44 tff(31,plain,
% 0.18/0.44 (~v3_struct_0(A!0)),
% 0.18/0.44 inference(and_elim,[status(thm)],[28])).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(34,plain,
% 0.18/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0)))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[34, 32])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(37,plain,
% 0.18/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(C, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[37, 31, 30, 29, 19])).
% 0.18/0.45 tff(39,plain,
% 0.18/0.45 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.45 inference(and_elim,[status(thm)],[28])).
% 0.18/0.45 tff(40,plain,
% 0.18/0.45 (v1_tsp_2(B!1, A!0)),
% 0.18/0.45 inference(and_elim,[status(thm)],[28])).
% 0.18/0.45 tff(41,plain,
% 0.18/0.45 (((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))) <=> ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(42,plain,
% 0.18/0.45 (((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v3_pre_topc(C, A!0)))) <=> ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(43,plain,
% 0.18/0.45 (((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v3_pre_topc(C, A!0))))) <=> ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[42])).
% 0.18/0.45 tff(44,plain,
% 0.18/0.45 (((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v3_pre_topc(C, A!0))))) <=> ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[43, 41])).
% 0.18/0.45 tff(45,plain,
% 0.18/0.45 ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v3_pre_topc(C, A!0))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(46,plain,
% 0.18/0.45 ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v3_pre_topc(C, A!0))))) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.45 tff(47,plain,
% 0.18/0.45 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[46, 40, 39, 38])).
% 0.18/0.45 tff(48,plain,
% 0.18/0.45 (^[A: $i, B: $i] : refl((m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 (![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.45 tff(50,plain,
% 0.18/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))), (((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(51,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[50])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(53,plain,
% 0.18/0.45 (^[A: $i, B: $i] : rewrite(((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.45 tff(55,axiom,(![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tops_1')).
% 0.18/0.45 tff(56,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.18/0.45 tff(58,plain,(
% 0.18/0.45 ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[57])).
% 0.18/0.45 tff(59,plain,
% 0.18/0.45 (![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.18/0.45 tff(60,plain,
% 0.18/0.45 (![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 (~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))),
% 0.18/0.45 inference(and_elim,[status(thm)],[28])).
% 0.18/0.45 tff(62,plain,
% 0.18/0.45 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.45 inference(or_elim,[status(thm)],[61])).
% 0.18/0.45 tff(63,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 ((m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[64])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[65, 63])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : (m1_subset_1(k1_tops_1(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.45 tff(69,plain,
% 0.18/0.45 (m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[68, 29, 62, 60])).
% 0.18/0.45 tff(70,plain,
% 0.18/0.45 (^[A: $i, B: $i] : refl((v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(71,plain,
% 0.18/0.45 (![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.45 tff(72,plain,
% 0.18/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A)) <=> (((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | v3_pre_topc(k1_tops_1(A, B), A)))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | v3_pre_topc(k1_tops_1(A, B), A)) <=> (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A)) <=> (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(73,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A)) <=> ![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.45 tff(74,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(75,plain,
% 0.18/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_pre_topc(k1_tops_1(A, B), A)) <=> ((v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_pre_topc(k1_tops_1(A, B), A)))), rewrite(((v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_pre_topc(k1_tops_1(A, B), A)) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))), ((((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_pre_topc(k1_tops_1(A, B), A)) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(76,plain,
% 0.18/0.45 (![A: $i, B: $i] : (((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_pre_topc(k1_tops_1(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.45 tff(77,axiom,(![A: $i, B: $i] : (((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_pre_topc(k1_tops_1(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_tops_1')).
% 0.18/0.45 tff(78,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.45 tff(79,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.18/0.45 tff(80,plain,(
% 0.18/0.45 ![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_pre_topc(k1_tops_1(A, B), A))),
% 0.18/0.45 inference(skolemize,[status(sab)],[79])).
% 0.18/0.45 tff(81,plain,
% 0.18/0.45 (![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.18/0.45 tff(82,plain,
% 0.18/0.45 (![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.18/0.45 tff(83,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | v3_pre_topc(k1_tops_1(A!0, C!2), A!0))) <=> ((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | v3_pre_topc(k1_tops_1(A!0, C!2), A!0))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(84,plain,
% 0.18/0.45 ((v3_pre_topc(k1_tops_1(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | v3_pre_topc(k1_tops_1(A!0, C!2), A!0))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(85,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_pre_topc(k1_tops_1(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | v3_pre_topc(k1_tops_1(A!0, C!2), A!0)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[84])).
% 0.18/0.45 tff(86,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_pre_topc(k1_tops_1(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | v3_pre_topc(k1_tops_1(A!0, C!2), A!0))),
% 0.18/0.45 inference(transitivity,[status(thm)],[85, 83])).
% 0.18/0.45 tff(87,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_pre_topc(k1_tops_1(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(88,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : (v3_pre_topc(k1_tops_1(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | v3_pre_topc(k1_tops_1(A!0, C!2), A!0)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.45 tff(89,plain,
% 0.18/0.45 (v3_pre_topc(k1_tops_1(A!0, C!2), A!0)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[88, 30, 29, 62, 82])).
% 0.18/0.45 tff(90,plain,
% 0.18/0.45 (~(k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2))))),
% 0.18/0.45 inference(or_elim,[status(thm)],[61])).
% 0.18/0.45 tff(91,plain,
% 0.18/0.45 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))) | (~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))) | (~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(92,plain,
% 0.18/0.45 (((~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2))))) <=> ((k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))) | (~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(93,plain,
% 0.18/0.45 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))) | (~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.46 tff(94,plain,
% 0.18/0.46 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))) | (~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[93, 91])).
% 0.18/0.46 tff(95,plain,
% 0.18/0.46 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0)) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(96,plain,
% 0.18/0.46 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | (k1_tops_1(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k1_tops_1(A!0, C!2)))) | (~m1_subset_1(k1_tops_1(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(k1_tops_1(A!0, C!2), A!0))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.46 tff(97,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[96, 90, 89, 69, 47])).
% 0.18/0.46 % SZS output end Proof
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------