%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP028+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 05:42:39 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP028+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:52:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(v1_tsp_2_type, type, (
% 0.11/0.38 v1_tsp_2: ( $i * $i ) > $o)).
% 0.11/0.38 tff(tptp_fun_A_0_type, type, (
% 0.11/0.38 tptp_fun_A_0: $i)).
% 0.11/0.38 tff(tptp_fun_C_16_type, type, (
% 0.11/0.38 tptp_fun_C_16: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_B_13_type, type, (
% 0.11/0.38 tptp_fun_B_13: $i > $i)).
% 0.11/0.38 tff(r1_tarski_type, type, (
% 0.11/0.38 r1_tarski: ( $i * $i ) > $o)).
% 0.11/0.38 tff(m1_subset_1_type, type, (
% 0.11/0.38 m1_subset_1: ( $i * $i ) > $o)).
% 0.11/0.38 tff(k1_zfmisc_1_type, type, (
% 0.11/0.38 k1_zfmisc_1: $i > $i)).
% 0.11/0.38 tff(u1_struct_0_type, type, (
% 0.11/0.38 u1_struct_0: $i > $i)).
% 0.11/0.38 tff(v1_tsp_1_type, type, (
% 0.11/0.38 v1_tsp_1: ( $i * $i ) > $o)).
% 0.11/0.38 tff(v3_tex_2_type, type, (
% 0.11/0.38 v3_tex_2: ( $i * $i ) > $o)).
% 0.11/0.38 tff(v1_xboole_0_type, type, (
% 0.11/0.38 v1_xboole_0: $i > $o)).
% 0.11/0.38 tff(v3_tops_1_type, type, (
% 0.11/0.38 v3_tops_1: ( $i * $i ) > $o)).
% 0.11/0.38 tff(v2_tops_1_type, type, (
% 0.11/0.38 v2_tops_1: ( $i * $i ) > $o)).
% 0.11/0.38 tff(v5_membered_type, type, (
% 0.11/0.38 v5_membered: $i > $o)).
% 0.11/0.38 tff(v4_membered_type, type, (
% 0.11/0.38 v4_membered: $i > $o)).
% 0.11/0.38 tff(v3_membered_type, type, (
% 0.11/0.38 v3_membered: $i > $o)).
% 0.11/0.38 tff(v2_membered_type, type, (
% 0.11/0.38 v2_membered: $i > $o)).
% 0.11/0.38 tff(v1_membered_type, type, (
% 0.11/0.38 v1_membered: $i > $o)).
% 0.11/0.38 tff(v4_pre_topc_type, type, (
% 0.11/0.38 v4_pre_topc: ( $i * $i ) > $o)).
% 0.11/0.38 tff(v3_pre_topc_type, type, (
% 0.11/0.38 v3_pre_topc: ( $i * $i ) > $o)).
% 0.11/0.38 tff(v2_pre_topc_type, type, (
% 0.11/0.38 v2_pre_topc: $i > $o)).
% 0.11/0.38 tff(l1_pre_topc_type, type, (
% 0.11/0.38 l1_pre_topc: $i > $o)).
% 0.11/0.38 tff(v3_struct_0_type, type, (
% 0.11/0.38 v3_struct_0: $i > $o)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[A: $i] : refl(((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A))))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_pre_topc(A) & l1_pre_topc(A)) <=> (~((~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~(v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~((~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~((~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~(v2_pre_topc(A) & l1_pre_topc(A))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_13(A)) & v3_pre_topc(tptp_fun_B_13(A), A) & v4_pre_topc(tptp_fun_B_13(A), A) & v1_membered(tptp_fun_B_13(A)) & v2_membered(tptp_fun_B_13(A)) & v3_membered(tptp_fun_B_13(A)) & v4_membered(tptp_fun_B_13(A)) & v5_membered(tptp_fun_B_13(A)) & v2_tops_1(tptp_fun_B_13(A), A) & v3_tops_1(tptp_fun_B_13(A), A)) <=> (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A))))), (((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_13(A)) & v3_pre_topc(tptp_fun_B_13(A), A) & v4_pre_topc(tptp_fun_B_13(A), A) & v1_membered(tptp_fun_B_13(A)) & v2_membered(tptp_fun_B_13(A)) & v3_membered(tptp_fun_B_13(A)) & v4_membered(tptp_fun_B_13(A)) & v5_membered(tptp_fun_B_13(A)) & v2_tops_1(tptp_fun_B_13(A), A) & v3_tops_1(tptp_fun_B_13(A), A))) <=> (((~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A))))))), rewrite((((~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A))))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))), (((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_13(A)) & v3_pre_topc(tptp_fun_B_13(A), A) & v4_pre_topc(tptp_fun_B_13(A), A) & v1_membered(tptp_fun_B_13(A)) & v2_membered(tptp_fun_B_13(A)) & v3_membered(tptp_fun_B_13(A)) & v4_membered(tptp_fun_B_13(A)) & v5_membered(tptp_fun_B_13(A)) & v2_tops_1(tptp_fun_B_13(A), A) & v3_tops_1(tptp_fun_B_13(A), A))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_13(A)) & v3_pre_topc(tptp_fun_B_13(A), A) & v4_pre_topc(tptp_fun_B_13(A), A) & v1_membered(tptp_fun_B_13(A)) & v2_membered(tptp_fun_B_13(A)) & v3_membered(tptp_fun_B_13(A)) & v4_membered(tptp_fun_B_13(A)) & v5_membered(tptp_fun_B_13(A)) & v2_tops_1(tptp_fun_B_13(A), A) & v3_tops_1(tptp_fun_B_13(A), A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))) <=> ![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A))), ((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A))), ((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A)))), (((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A)) & v1_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A)) & v1_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B))), (((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B)))), ((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B)) & v2_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B)) & v2_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B))), ((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B)))), (((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B)) & v3_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B)) & v3_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B))), (((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B)))), ((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B)) & v4_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B)) & v4_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B))), ((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B)))), (((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B)) & v5_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B)) & v5_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B))), (((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B)))), ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B)) & v2_tops_1(B, A)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B)) & v2_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A))), ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A)))), (((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A)) & v3_tops_1(B, A)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))), (((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))))), (?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))), (((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A))) <=> ((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))))), rewrite(((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))), (((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A))) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![A: $i] : ((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A))) <=> ![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.38 tff(8,axiom,(![A: $i] : ((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc5_tops_1')).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.38 tff(11,plain,(
% 0.11/0.38 ![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_13(A)) & v3_pre_topc(tptp_fun_B_13(A), A) & v4_pre_topc(tptp_fun_B_13(A), A) & v1_membered(tptp_fun_B_13(A)) & v2_membered(tptp_fun_B_13(A)) & v3_membered(tptp_fun_B_13(A)) & v4_membered(tptp_fun_B_13(A)) & v5_membered(tptp_fun_B_13(A)) & v2_tops_1(tptp_fun_B_13(A), A) & v3_tops_1(tptp_fun_B_13(A), A)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & 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)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & 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))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 ((~![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)))) <=> (~![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))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 ((~![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)))) <=> (~![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))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(17,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_tsp_2')).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (~![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (~![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (~![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (~![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & 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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (l1_pre_topc(A!0)),
% 0.11/0.38 inference(and_elim,[status(thm)],[22])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (v2_pre_topc(A!0)),
% 0.11/0.38 inference(and_elim,[status(thm)],[22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))) | ((~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 ((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))) | ((~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 ((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_13(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_13(A))) | (~v3_pre_topc(tptp_fun_B_13(A), A)) | (~v4_pre_topc(tptp_fun_B_13(A), A)) | (~v1_membered(tptp_fun_B_13(A))) | (~v2_membered(tptp_fun_B_13(A))) | (~v3_membered(tptp_fun_B_13(A))) | (~v4_membered(tptp_fun_B_13(A))) | (~v5_membered(tptp_fun_B_13(A))) | (~v2_tops_1(tptp_fun_B_13(A), A)) | (~v3_tops_1(tptp_fun_B_13(A), A)))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (~((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[27, 24, 23, 13])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0))) | v1_xboole_0(tptp_fun_B_13(A!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (v1_xboole_0(tptp_fun_B_13(A!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~v3_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_13(A!0), A!0)) | (~v1_membered(tptp_fun_B_13(A!0))) | (~v2_membered(tptp_fun_B_13(A!0))) | (~v3_membered(tptp_fun_B_13(A!0))) | (~v4_membered(tptp_fun_B_13(A!0))) | (~v5_membered(tptp_fun_B_13(A!0))) | (~v2_tops_1(tptp_fun_B_13(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_13(A!0), A!0))) | m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[36, 34])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)) <=> (((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))), rewrite((((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)) <=> ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)) <=> ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), (![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)) <=> ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : rewrite(((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_tex_2(B, A)) <=> ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))), (![B: $i] : ((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_tex_2(B, A)) <=> ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_tex_2(B, A))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_tex_2(B, A))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_tex_2(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.38 tff(43,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v3_tex_2(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_tex_2')).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.11/0.38 tff(46,plain,(
% 0.11/0.38 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~(v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v3_tex_2(B, A)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[45])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (~v3_struct_0(A!0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[22])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_xboole_0(B)) | v3_tex_2(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 49, 24, 23, 48])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (((~![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))) | ((~v1_xboole_0(tptp_fun_B_13(A!0))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(tptp_fun_B_13(A!0), A!0))) <=> ((~![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(tptp_fun_B_13(A!0), A!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))) | ((~v1_xboole_0(tptp_fun_B_13(A!0))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(tptp_fun_B_13(A!0), A!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))) | (~v1_xboole_0(tptp_fun_B_13(A!0))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(tptp_fun_B_13(A!0), A!0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (v3_tex_2(tptp_fun_B_13(A!0), A!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 56, 32, 30])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v3_tex_2(B, A) => v1_tsp_1(B, A)) <=> ((~v3_tex_2(B, A)) | v1_tsp_1(B, A))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_tex_2(B, A)) | v1_tsp_1(B, A))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_tex_2(B, A)) | v1_tsp_1(B, A))) <=> (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A))) <=> (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A))) <=> ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A)))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A)))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A)))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.39 tff(71,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_tex_2(B, A) => v1_tsp_1(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t11_tsp_1')).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.39 tff(74,plain,(
% 0.19/0.39 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[73])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : (v1_tsp_1(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_tex_2(B, A!0)))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : (v1_tsp_1(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_tex_2(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : (v1_tsp_1(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_tex_2(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : (v1_tsp_1(B, A!0) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_tex_2(B, A!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : (v1_tsp_1(B, A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_tex_2(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[82, 49, 23, 76])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))) | ((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_B_13(A!0), A!0) | (~v3_tex_2(tptp_fun_B_13(A!0), A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_B_13(A!0), A!0) | (~v3_tex_2(tptp_fun_B_13(A!0), A!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))) | ((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_B_13(A!0), A!0) | (~v3_tex_2(tptp_fun_B_13(A!0), A!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(B, A!0) | (~v3_tex_2(B, A!0)))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | v1_tsp_1(tptp_fun_B_13(A!0), A!0) | (~v3_tex_2(tptp_fun_B_13(A!0), A!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (v1_tsp_1(tptp_fun_B_13(A!0), A!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 83, 32, 60])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))))) <=> (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))), (((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))), rewrite(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))), (((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), 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_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), 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_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (![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_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ((~v1_tsp_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (![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_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (![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_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (^[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(rewrite((~(v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(C, A)))))) <=> (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(C, A))))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(C, A))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(C, A))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(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_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(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_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 (![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_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(C, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(v1_tsp_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.39 tff(100,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_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (~(r1_tarski(B, C) & v1_tsp_2(C, A))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9_tsp_2')).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (![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_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (![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_1(B, A) & ![C: $i] : ((~(r1_tarski(B, C) & v1_tsp_2(C, A))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.39 tff(103,plain,(
% 0.19/0.39 ![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_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[102])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (![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_1(B, A)) | (~((~(r1_tarski(B, tptp_fun_C_16(B, A)) & v1_tsp_2(tptp_fun_C_16(B, A), A))) | (~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[105, 92])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(B, A)) | (~((~m1_subset_1(tptp_fun_C_16(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, tptp_fun_C_16(B, A))) | (~v1_tsp_2(tptp_fun_C_16(B, A), A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[109, 49, 24, 23, 106])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0)))))) | ((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_B_13(A!0), A!0)) | (~((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0)))))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_B_13(A!0), A!0)) | (~((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0)))))) | ((~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_B_13(A!0), A!0)) | (~((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(B, A!0)) | (~((~m1_subset_1(tptp_fun_C_16(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, tptp_fun_C_16(B, A!0))) | (~v1_tsp_2(tptp_fun_C_16(B, A!0), A!0)))))) | (~m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_B_13(A!0), A!0)) | (~((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 (~((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[113, 110, 32, 87])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 (((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0))) | v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 (v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 (((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(tptp_fun_B_13(A!0), tptp_fun_C_16(tptp_fun_B_13(A!0), A!0))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0))) | m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (^[B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (^[B: $i] : trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))) & v1_tsp_2(B, A!0)) <=> (~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0))))), ((~(m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))) & v1_tsp_2(B, A!0))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))), ((~(m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))) & v1_tsp_2(B, A!0))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (![B: $i] : (~(m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))) & v1_tsp_2(B, A!0))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (![B: $i] : (~(m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))) & v1_tsp_2(B, A!0)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[22])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))) | ((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))) | (~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))) | ((~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))) | (~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[128, 125, 118, 116])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------