TSTP Solution File: TOP028+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP028+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 30 01:55:54 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : TOP028+1 : TPTP v8.1.0. Released v3.4.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 09:49:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(v1_tsp_2_type, type, (
% 0.19/0.46 v1_tsp_2: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_A_0_type, type, (
% 0.19/0.46 tptp_fun_A_0: $i)).
% 0.19/0.46 tff(tptp_fun_C_16_type, type, (
% 0.19/0.46 tptp_fun_C_16: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_B_13_type, type, (
% 0.19/0.46 tptp_fun_B_13: $i > $i)).
% 0.19/0.46 tff(r1_tarski_type, type, (
% 0.19/0.46 r1_tarski: ( $i * $i ) > $o)).
% 0.19/0.46 tff(m1_subset_1_type, type, (
% 0.19/0.46 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.46 tff(k1_zfmisc_1_type, type, (
% 0.19/0.46 k1_zfmisc_1: $i > $i)).
% 0.19/0.46 tff(u1_struct_0_type, type, (
% 0.19/0.46 u1_struct_0: $i > $i)).
% 0.19/0.46 tff(v1_tsp_1_type, type, (
% 0.19/0.46 v1_tsp_1: ( $i * $i ) > $o)).
% 0.19/0.46 tff(v3_tex_2_type, type, (
% 0.19/0.46 v3_tex_2: ( $i * $i ) > $o)).
% 0.19/0.46 tff(v1_xboole_0_type, type, (
% 0.19/0.46 v1_xboole_0: $i > $o)).
% 0.19/0.46 tff(v3_tops_1_type, type, (
% 0.19/0.46 v3_tops_1: ( $i * $i ) > $o)).
% 0.19/0.46 tff(v2_tops_1_type, type, (
% 0.19/0.46 v2_tops_1: ( $i * $i ) > $o)).
% 0.19/0.46 tff(v5_membered_type, type, (
% 0.19/0.46 v5_membered: $i > $o)).
% 0.19/0.46 tff(v4_membered_type, type, (
% 0.19/0.46 v4_membered: $i > $o)).
% 0.19/0.46 tff(v3_membered_type, type, (
% 0.19/0.46 v3_membered: $i > $o)).
% 0.19/0.46 tff(v2_membered_type, type, (
% 0.19/0.46 v2_membered: $i > $o)).
% 0.19/0.46 tff(v1_membered_type, type, (
% 0.19/0.46 v1_membered: $i > $o)).
% 0.19/0.46 tff(v4_pre_topc_type, type, (
% 0.19/0.46 v4_pre_topc: ( $i * $i ) > $o)).
% 0.19/0.46 tff(v3_pre_topc_type, type, (
% 0.19/0.46 v3_pre_topc: ( $i * $i ) > $o)).
% 0.19/0.46 tff(v2_pre_topc_type, type, (
% 0.19/0.46 v2_pre_topc: $i > $o)).
% 0.19/0.46 tff(l1_pre_topc_type, type, (
% 0.19/0.46 l1_pre_topc: $i > $o)).
% 0.19/0.46 tff(v3_struct_0_type, type, (
% 0.19/0.46 v3_struct_0: $i > $o)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (^[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))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (^[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)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(6,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.46 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')).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.46 tff(11,plain,(
% 0.19/0.46 ![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)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[10])).
% 0.19/0.46 tff(12,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 ((((~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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 ((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (((~(~((~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))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (((~(~((~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))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B, A)))) <=> (~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B, A)))) <=> (~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(20,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')).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 ((~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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (l1_pre_topc(A!0)),
% 0.19/0.47 inference(and_elim,[status(thm)],[28])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (v2_pre_topc(A!0)),
% 0.19/0.47 inference(and_elim,[status(thm)],[28])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (((~![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)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 ((~![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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 ((~![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (~((~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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[33, 30, 29, 13])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (v1_xboole_0(tptp_fun_B_13(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (((~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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (m1_subset_1(tptp_fun_B_13(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (^[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))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.47 tff(49,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')).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.47 tff(52,plain,(
% 0.19/0.47 ![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)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[51])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (~v3_struct_0(A!0)),
% 0.19/0.47 inference(and_elim,[status(thm)],[28])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 ((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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 ((~![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))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.48 tff(62,plain,
% 0.19/0.48 (![B: $i] : ((~v1_xboole_0(B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | v3_tex_2(B, A!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[61, 55, 30, 29, 54])).
% 0.19/0.48 tff(63,plain,
% 0.19/0.48 (((~![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))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(64,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(65,plain,
% 0.19/0.48 ((~![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)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 (v3_tex_2(tptp_fun_B_13(A!0), A!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[65, 62, 38, 36])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.48 tff(77,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')).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.48 tff(80,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[79])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 ((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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[88, 55, 29, 82])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (v1_tsp_1(tptp_fun_B_13(A!0), A!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[92, 89, 38, 66])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (^[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))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (^[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)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (![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)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 (^[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)))))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (![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)))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.49 tff(106,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')).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (![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)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 (![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)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.19/0.49 tff(109,plain,(
% 0.19/0.49 ![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)))))))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[108])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (![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))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (![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))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (![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))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[111, 98])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (((~![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))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 ((~![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))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[115, 55, 30, 29, 112])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (((~![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 ((~![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 (~((~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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[119, 116, 38, 93])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (((~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)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 (((~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)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 (m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (![B: $i] : (~(m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))) & v1_tsp_2(B, A!0)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[28])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(B, A!0)))) | (~m1_subset_1(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_2(tptp_fun_C_16(tptp_fun_B_13(A!0), A!0), A!0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[134, 131, 124, 122])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------