TSTP Solution File: TOP033+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP033+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 01:55:57 EDT 2022
% Result : Theorem 19.25s 12.50s
% Output : Proof 19.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP033+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.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 10:17:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 19.25/12.50 % SZS status Theorem
% 19.25/12.50 % SZS output start Proof
% 19.25/12.50 tff(k1_struct_0_type, type, (
% 19.25/12.50 k1_struct_0: ( $i * $i ) > $i)).
% 19.25/12.50 tff(k8_funct_2_type, type, (
% 19.25/12.50 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 19.25/12.50 tff(tptp_fun_E_25_type, type, (
% 19.25/12.50 tptp_fun_E_25: ( $i * $i * $i * $i ) > $i)).
% 19.25/12.50 tff(tptp_fun_A_0_type, type, (
% 19.25/12.50 tptp_fun_A_0: $i)).
% 19.25/12.50 tff(tptp_fun_B_1_type, type, (
% 19.25/12.50 tptp_fun_B_1: $i)).
% 19.25/12.50 tff(tptp_fun_C_2_type, type, (
% 19.25/12.50 tptp_fun_C_2: $i)).
% 19.25/12.50 tff(u1_struct_0_type, type, (
% 19.25/12.50 u1_struct_0: $i > $i)).
% 19.25/12.50 tff(k5_subset_1_type, type, (
% 19.25/12.50 k5_subset_1: ( $i * $i * $i ) > $i)).
% 19.25/12.50 tff(k4_tex_4_type, type, (
% 19.25/12.50 k4_tex_4: ( $i * $i ) > $i)).
% 19.25/12.50 tff(k1_tarski_type, type, (
% 19.25/12.50 k1_tarski: $i > $i)).
% 19.25/12.50 tff(m1_subset_1_type, type, (
% 19.25/12.50 m1_subset_1: ( $i * $i ) > $o)).
% 19.25/12.50 tff(k1_zfmisc_1_type, type, (
% 19.25/12.50 k1_zfmisc_1: $i > $i)).
% 19.25/12.50 tff(v3_borsuk_1_type, type, (
% 19.25/12.50 v3_borsuk_1: ( $i * $i * $i ) > $o)).
% 19.25/12.50 tff(m2_relset_1_type, type, (
% 19.25/12.50 m2_relset_1: ( $i * $i * $i ) > $o)).
% 19.25/12.50 tff(v5_pre_topc_type, type, (
% 19.25/12.50 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 19.25/12.50 tff(v1_funct_2_type, type, (
% 19.25/12.50 v1_funct_2: ( $i * $i * $i ) > $o)).
% 19.25/12.50 tff(v1_funct_1_type, type, (
% 19.25/12.50 v1_funct_1: $i > $o)).
% 19.25/12.50 tff(m2_tsp_1_type, type, (
% 19.25/12.50 m2_tsp_1: ( $i * $i ) > $o)).
% 19.25/12.50 tff(v2_tsp_2_type, type, (
% 19.25/12.50 v2_tsp_2: ( $i * $i ) > $o)).
% 19.25/12.50 tff(v3_struct_0_type, type, (
% 19.25/12.50 v3_struct_0: $i > $o)).
% 19.25/12.50 tff(v2_pre_topc_type, type, (
% 19.25/12.50 v2_pre_topc: $i > $o)).
% 19.25/12.50 tff(l1_pre_topc_type, type, (
% 19.25/12.50 l1_pre_topc: $i > $o)).
% 19.25/12.50 tff(r2_hidden_type, type, (
% 19.25/12.50 r2_hidden: ( $i * $i ) > $o)).
% 19.25/12.50 tff(m1_pre_topc_type, type, (
% 19.25/12.50 m1_pre_topc: ( $i * $i ) > $o)).
% 19.25/12.50 tff(m1_relset_1_type, type, (
% 19.25/12.50 m1_relset_1: ( $i * $i * $i ) > $o)).
% 19.25/12.50 tff(v1_xboole_0_type, type, (
% 19.25/12.50 v1_xboole_0: $i > $o)).
% 19.25/12.50 tff(l1_struct_0_type, type, (
% 19.25/12.50 l1_struct_0: $i > $o)).
% 19.25/12.50 tff(k1_funct_1_type, type, (
% 19.25/12.50 k1_funct_1: ( $i * $i ) > $i)).
% 19.25/12.50 tff(r1_tarski_type, type, (
% 19.25/12.50 r1_tarski: ( $i * $i ) > $o)).
% 19.25/12.50 tff(tptp_fun_C_4_type, type, (
% 19.25/12.50 tptp_fun_C_4: ( $i * $i ) > $i)).
% 19.25/12.50 tff(v1_tsp_1_type, type, (
% 19.25/12.50 v1_tsp_1: ( $i * $i ) > $o)).
% 19.25/12.50 tff(tptp_fun_C_3_type, type, (
% 19.25/12.50 tptp_fun_C_3: ( $i * $i ) > $i)).
% 19.25/12.50 tff(v1_tsp_2_type, type, (
% 19.25/12.50 v1_tsp_2: ( $i * $i ) > $o)).
% 19.25/12.50 tff(tptp_fun_C_5_type, type, (
% 19.25/12.50 tptp_fun_C_5: ( $i * $i ) > $i)).
% 19.25/12.50 tff(k2_tex_4_type, type, (
% 19.25/12.50 k2_tex_4: ( $i * $i ) > $i)).
% 19.25/12.50 tff(1,plain,
% 19.25/12.50 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))))))),
% 19.25/12.50 inference(bind,[status(th)],[])).
% 19.25/12.50 tff(2,plain,
% 19.25/12.50 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))),
% 19.25/12.50 inference(quant_intro,[status(thm)],[1])).
% 19.25/12.50 tff(3,plain,
% 19.25/12.50 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.50 inference(bind,[status(th)],[])).
% 19.25/12.50 tff(4,plain,
% 19.25/12.50 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 19.25/12.50 inference(quant_intro,[status(thm)],[3])).
% 19.25/12.50 tff(5,plain,
% 19.25/12.50 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.50 inference(bind,[status(th)],[])).
% 19.25/12.50 tff(6,plain,
% 19.25/12.50 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 19.25/12.50 inference(quant_intro,[status(thm)],[5])).
% 19.25/12.50 tff(7,plain,
% 19.25/12.50 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 19.25/12.50 inference(transitivity,[status(thm)],[6, 4])).
% 19.25/12.50 tff(8,plain,
% 19.25/12.50 (^[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(((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))) <=> (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))) <=> (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))) <=> ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 19.25/12.50 inference(bind,[status(th)],[])).
% 19.25/12.50 tff(9,plain,
% 19.25/12.50 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 19.25/12.50 inference(quant_intro,[status(thm)],[8])).
% 19.25/12.50 tff(10,plain,
% 19.25/12.50 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | ((~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A)))))))))))),
% 19.25/12.50 inference(bind,[status(th)],[])).
% 19.25/12.50 tff(11,plain,
% 19.25/12.50 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | ((~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))),
% 19.25/12.50 inference(quant_intro,[status(thm)],[10])).
% 19.25/12.50 tff(12,plain,
% 19.25/12.50 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))),
% 19.25/12.50 inference(rewrite,[status(thm)],[])).
% 19.25/12.50 tff(13,plain,
% 19.25/12.50 (^[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((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) <=> ((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) <=> ((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))), ((((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)) <=> (((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))), rewrite((((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)) <=> ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B))), ((((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)) <=> ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B)))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B))))), rewrite((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B))) <=> (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 19.25/12.51 inference(bind,[status(th)],[])).
% 19.25/12.51 tff(14,plain,
% 19.25/12.51 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))),
% 19.25/12.51 inference(quant_intro,[status(thm)],[13])).
% 19.25/12.51 tff(15,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_tsp_2')).
% 19.25/12.51 tff(16,plain,
% 19.25/12.51 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[15, 14])).
% 19.25/12.51 tff(17,plain,
% 19.25/12.51 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[16, 12])).
% 19.25/12.51 tff(18,plain,(
% 19.25/12.51 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | ((~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))),
% 19.25/12.51 inference(skolemize,[status(sab)],[17])).
% 19.25/12.51 tff(19,plain,
% 19.25/12.51 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[18, 11])).
% 19.25/12.51 tff(20,plain,
% 19.25/12.51 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[19, 9])).
% 19.25/12.51 tff(21,plain,
% 19.25/12.51 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[20, 7])).
% 19.25/12.51 tff(22,plain,
% 19.25/12.51 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[21, 2])).
% 19.25/12.51 tff(23,plain,
% 19.25/12.51 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(24,plain,
% 19.25/12.51 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(25,plain,
% 19.25/12.51 (((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(26,plain,
% 19.25/12.51 ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(27,plain,
% 19.25/12.51 (((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 19.25/12.51 inference(monotonicity,[status(thm)],[26])).
% 19.25/12.51 tff(28,plain,
% 19.25/12.51 (((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(transitivity,[status(thm)],[27, 25])).
% 19.25/12.51 tff(29,plain,
% 19.25/12.51 ((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(30,plain,
% 19.25/12.51 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 19.25/12.51 inference(monotonicity,[status(thm)],[29, 28])).
% 19.25/12.51 tff(31,plain,
% 19.25/12.51 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(transitivity,[status(thm)],[30, 24])).
% 19.25/12.51 tff(32,plain,
% 19.25/12.51 ((~(~((~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))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(33,plain,
% 19.25/12.51 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 19.25/12.51 inference(monotonicity,[status(thm)],[32, 31])).
% 19.25/12.51 tff(34,plain,
% 19.25/12.51 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.51 inference(transitivity,[status(thm)],[33, 23])).
% 19.25/12.51 tff(35,plain,
% 19.25/12.51 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(36,plain,
% 19.25/12.51 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D))) => v3_borsuk_1(C, A, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(37,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D))) => v3_borsuk_1(C, A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_tsp_2')).
% 19.25/12.51 tff(38,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[37, 36])).
% 19.25/12.51 tff(39,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[38, 35])).
% 19.25/12.51 tff(40,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[39, 35])).
% 19.25/12.51 tff(41,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[40, 35])).
% 19.25/12.51 tff(42,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[41, 35])).
% 19.25/12.51 tff(43,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[42, 35])).
% 19.25/12.51 tff(44,plain,
% 19.25/12.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[43, 35])).
% 19.25/12.51 tff(45,plain,
% 19.25/12.51 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.51 inference(modus_ponens,[status(thm)],[44, 34])).
% 19.25/12.51 tff(46,plain,
% 19.25/12.51 (l1_pre_topc(A!0)),
% 19.25/12.51 inference(and_elim,[status(thm)],[45])).
% 19.25/12.51 tff(47,plain,
% 19.25/12.51 (v2_pre_topc(A!0)),
% 19.25/12.51 inference(and_elim,[status(thm)],[45])).
% 19.25/12.51 tff(48,plain,
% 19.25/12.51 (~v3_struct_0(A!0)),
% 19.25/12.51 inference(and_elim,[status(thm)],[45])).
% 19.25/12.51 tff(49,plain,
% 19.25/12.51 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(50,plain,
% 19.25/12.51 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))),
% 19.25/12.51 inference(rewrite,[status(thm)],[])).
% 19.25/12.51 tff(51,plain,
% 19.25/12.51 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))))),
% 19.25/12.51 inference(monotonicity,[status(thm)],[50])).
% 19.25/12.51 tff(52,plain,
% 19.25/12.51 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))),
% 19.25/12.52 inference(transitivity,[status(thm)],[51, 49])).
% 19.25/12.52 tff(53,plain,
% 19.25/12.52 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0))))))))))),
% 19.25/12.52 inference(quant_inst,[status(thm)],[])).
% 19.25/12.52 tff(54,plain,
% 19.25/12.52 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(D = u1_struct_0(B))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, tptp_fun_E_25(D, C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))),
% 19.25/12.52 inference(modus_ponens,[status(thm)],[53, 52])).
% 19.25/12.52 tff(55,plain,
% 19.25/12.52 (![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))),
% 19.25/12.52 inference(unit_resolution,[status(thm)],[54, 48, 47, 46, 22])).
% 19.25/12.52 tff(56,plain,
% 19.25/12.52 (m2_tsp_1(B!1, A!0)),
% 19.25/12.52 inference(and_elim,[status(thm)],[45])).
% 19.25/12.52 tff(57,plain,
% 19.25/12.52 (v2_tsp_2(B!1, A!0)),
% 19.25/12.52 inference(and_elim,[status(thm)],[45])).
% 19.25/12.52 tff(58,plain,
% 19.25/12.52 (~v3_struct_0(B!1)),
% 19.25/12.52 inference(and_elim,[status(thm)],[45])).
% 19.25/12.52 tff(59,plain,
% 19.25/12.52 (((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))),
% 19.25/12.52 inference(rewrite,[status(thm)],[])).
% 19.25/12.52 tff(60,plain,
% 19.25/12.52 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))),
% 19.25/12.52 inference(rewrite,[status(thm)],[])).
% 19.25/12.52 tff(61,plain,
% 19.25/12.52 (^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite(((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))), (![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))) <=> ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))), (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))), rewrite(((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))), (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))))),
% 19.25/12.52 inference(bind,[status(th)],[])).
% 19.25/12.52 tff(62,plain,
% 19.25/12.52 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))),
% 19.25/12.52 inference(quant_intro,[status(thm)],[61])).
% 19.25/12.52 tff(63,plain,
% 19.25/12.52 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))),
% 19.25/12.52 inference(monotonicity,[status(thm)],[62])).
% 19.25/12.52 tff(64,plain,
% 19.25/12.52 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))),
% 19.25/12.52 inference(transitivity,[status(thm)],[63, 60])).
% 19.25/12.52 tff(65,plain,
% 19.25/12.52 (((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))))),
% 19.25/12.52 inference(monotonicity,[status(thm)],[64])).
% 19.25/12.52 tff(66,plain,
% 19.25/12.52 (((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))),
% 19.25/12.52 inference(transitivity,[status(thm)],[65, 59])).
% 19.25/12.52 tff(67,plain,
% 19.25/12.52 ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0)))))))))),
% 19.25/12.52 inference(quant_inst,[status(thm)],[])).
% 19.25/12.52 tff(68,plain,
% 19.25/12.52 ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | v3_borsuk_1(C, A!0, B) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(D, C, B, A!0)))))))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[67, 66])).
% 19.25/12.53 tff(69,plain,
% 19.25/12.53 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[68, 58, 57, 56, 55])).
% 19.25/12.53 tff(70,plain,
% 19.25/12.53 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.53 inference(and_elim,[status(thm)],[45])).
% 19.25/12.53 tff(71,plain,
% 19.25/12.53 (v5_pre_topc(C!2, A!0, B!1)),
% 19.25/12.53 inference(and_elim,[status(thm)],[45])).
% 19.25/12.53 tff(72,plain,
% 19.25/12.53 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.53 inference(and_elim,[status(thm)],[45])).
% 19.25/12.53 tff(73,plain,
% 19.25/12.53 (v1_funct_1(C!2)),
% 19.25/12.53 inference(and_elim,[status(thm)],[45])).
% 19.25/12.53 tff(74,plain,
% 19.25/12.53 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(75,plain,
% 19.25/12.53 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) <=> ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(76,plain,
% 19.25/12.53 (^[D: $i] : rewrite(((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))) <=> (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(77,plain,
% 19.25/12.53 (![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))) <=> ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[76])).
% 19.25/12.53 tff(78,plain,
% 19.25/12.53 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(monotonicity,[status(thm)],[77])).
% 19.25/12.53 tff(79,plain,
% 19.25/12.53 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) <=> ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(transitivity,[status(thm)],[78, 75])).
% 19.25/12.53 tff(80,plain,
% 19.25/12.53 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))))),
% 19.25/12.53 inference(monotonicity,[status(thm)],[79])).
% 19.25/12.53 tff(81,plain,
% 19.25/12.53 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(transitivity,[status(thm)],[80, 74])).
% 19.25/12.53 tff(82,plain,
% 19.25/12.53 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0))))))))),
% 19.25/12.53 inference(quant_inst,[status(thm)],[])).
% 19.25/12.53 tff(83,plain,
% 19.25/12.53 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | v3_borsuk_1(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_25(D, C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(D, C, B!1, A!0))))))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[82, 81])).
% 19.25/12.53 tff(84,plain,
% 19.25/12.53 (![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[83, 73, 72, 71, 70, 69])).
% 19.25/12.53 tff(85,plain,
% 19.25/12.53 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(86,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[85])).
% 19.25/12.53 tff(87,plain,
% 19.25/12.53 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(88,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[87])).
% 19.25/12.53 tff(89,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(transitivity,[status(thm)],[88, 86])).
% 19.25/12.53 tff(90,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(91,plain,
% 19.25/12.53 (^[A: $i] : rewrite((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(92,plain,
% 19.25/12.53 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[91])).
% 19.25/12.53 tff(93,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_tsp_1')).
% 19.25/12.53 tff(94,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[93, 92])).
% 19.25/12.53 tff(95,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[94, 90])).
% 19.25/12.53 tff(96,plain,(
% 19.25/12.53 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(skolemize,[status(sab)],[95])).
% 19.25/12.53 tff(97,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[96, 89])).
% 19.25/12.53 tff(98,plain,
% 19.25/12.53 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(99,plain,
% 19.25/12.53 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 19.25/12.53 inference(quant_inst,[status(thm)],[])).
% 19.25/12.53 tff(100,plain,
% 19.25/12.53 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[99, 98])).
% 19.25/12.53 tff(101,plain,
% 19.25/12.53 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[100, 46, 97])).
% 19.25/12.53 tff(102,plain,
% 19.25/12.53 ((~![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))) | (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))),
% 19.25/12.53 inference(quant_inst,[status(thm)],[])).
% 19.25/12.53 tff(103,plain,
% 19.25/12.53 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[102, 101])).
% 19.25/12.53 tff(104,plain,
% 19.25/12.53 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | (~m2_tsp_1(B!1, A!0)) | m1_pre_topc(B!1, A!0)),
% 19.25/12.53 inference(tautology,[status(thm)],[])).
% 19.25/12.53 tff(105,plain,
% 19.25/12.53 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[104, 56])).
% 19.25/12.53 tff(106,plain,
% 19.25/12.53 (m1_pre_topc(B!1, A!0)),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[105, 103])).
% 19.25/12.53 tff(107,plain,
% 19.25/12.53 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(108,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[107])).
% 19.25/12.53 tff(109,plain,
% 19.25/12.53 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(110,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[109])).
% 19.25/12.53 tff(111,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(transitivity,[status(thm)],[110, 108])).
% 19.25/12.53 tff(112,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(113,plain,
% 19.25/12.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 19.25/12.53 inference(bind,[status(th)],[])).
% 19.25/12.53 tff(114,plain,
% 19.25/12.53 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(quant_intro,[status(thm)],[113])).
% 19.25/12.53 tff(115,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_tsep_1')).
% 19.25/12.53 tff(116,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[115, 114])).
% 19.25/12.53 tff(117,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[116, 112])).
% 19.25/12.53 tff(118,plain,(
% 19.25/12.53 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(skolemize,[status(sab)],[117])).
% 19.25/12.53 tff(119,plain,
% 19.25/12.53 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[118, 111])).
% 19.25/12.53 tff(120,plain,
% 19.25/12.53 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(121,plain,
% 19.25/12.53 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 19.25/12.53 inference(quant_inst,[status(thm)],[])).
% 19.25/12.53 tff(122,plain,
% 19.25/12.53 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[121, 120])).
% 19.25/12.53 tff(123,plain,
% 19.25/12.53 (![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[122, 46, 119])).
% 19.25/12.53 tff(124,plain,
% 19.25/12.53 (((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 19.25/12.53 inference(rewrite,[status(thm)],[])).
% 19.25/12.53 tff(125,plain,
% 19.25/12.53 ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 19.25/12.53 inference(quant_inst,[status(thm)],[])).
% 19.25/12.53 tff(126,plain,
% 19.25/12.53 ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 19.25/12.53 inference(modus_ponens,[status(thm)],[125, 124])).
% 19.25/12.53 tff(127,plain,
% 19.25/12.53 ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[126, 123])).
% 19.25/12.53 tff(128,plain,
% 19.25/12.53 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 19.25/12.53 inference(unit_resolution,[status(thm)],[127, 106])).
% 19.25/12.53 tff(129,plain,
% 19.25/12.53 (~v3_borsuk_1(C!2, A!0, B!1)),
% 19.25/12.53 inference(and_elim,[status(thm)],[45])).
% 19.25/12.53 tff(130,plain,
% 19.25/12.53 (((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))) <=> ((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(131,plain,
% 19.25/12.54 ((v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | $false | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))) <=> (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(132,plain,
% 19.25/12.54 ((~$true) <=> $false),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(133,plain,
% 19.25/12.54 ((u1_struct_0(B!1) = u1_struct_0(B!1)) <=> $true),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(134,plain,
% 19.25/12.54 ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) <=> (~$true)),
% 19.25/12.54 inference(monotonicity,[status(thm)],[133])).
% 19.25/12.54 tff(135,plain,
% 19.25/12.54 ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) <=> $false),
% 19.25/12.54 inference(transitivity,[status(thm)],[134, 132])).
% 19.25/12.54 tff(136,plain,
% 19.25/12.54 ((v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))) <=> (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | $false | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.25/12.54 inference(monotonicity,[status(thm)],[135])).
% 19.25/12.54 tff(137,plain,
% 19.25/12.54 ((v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))) <=> (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.25/12.54 inference(transitivity,[status(thm)],[136, 131])).
% 19.25/12.54 tff(138,plain,
% 19.25/12.54 (((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))) <=> ((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))))),
% 19.25/12.54 inference(monotonicity,[status(thm)],[137])).
% 19.25/12.54 tff(139,plain,
% 19.25/12.54 (((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))) <=> ((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.25/12.54 inference(transitivity,[status(thm)],[138, 130])).
% 19.25/12.54 tff(140,plain,
% 19.25/12.54 ((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.25/12.54 inference(quant_inst,[status(thm)],[])).
% 19.25/12.54 tff(141,plain,
% 19.25/12.54 ((~![D: $i] : (v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(D = u1_struct_0(B!1))) | (~((~m1_subset_1(tptp_fun_E_25(D, C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), D, k4_tex_4(A!0, tptp_fun_E_25(D, C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(D, C!2, B!1, A!0)))))))) | v3_borsuk_1(C!2, A!0, B!1) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[140, 139])).
% 19.25/12.54 tff(142,plain,
% 19.25/12.54 (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[141, 129, 128, 84])).
% 19.25/12.54 tff(143,plain,
% 19.25/12.54 (((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))) | m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))),
% 19.25/12.54 inference(tautology,[status(thm)],[])).
% 19.25/12.54 tff(144,plain,
% 19.25/12.54 (m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[143, 142])).
% 19.25/12.54 tff(145,plain,
% 19.25/12.54 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(146,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[145])).
% 19.25/12.54 tff(147,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(148,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 19.25/12.54 tff(149,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[148, 147])).
% 19.25/12.54 tff(150,plain,(
% 19.25/12.54 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.25/12.54 inference(skolemize,[status(sab)],[149])).
% 19.25/12.54 tff(151,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[150, 146])).
% 19.25/12.54 tff(152,plain,
% 19.25/12.54 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.25/12.54 inference(quant_inst,[status(thm)],[])).
% 19.25/12.54 tff(153,plain,
% 19.25/12.54 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[152, 151])).
% 19.25/12.54 tff(154,plain,
% 19.25/12.54 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.54 inference(tautology,[status(thm)],[])).
% 19.25/12.54 tff(155,plain,
% 19.25/12.54 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[154, 70])).
% 19.25/12.54 tff(156,plain,
% 19.25/12.54 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[155, 153])).
% 19.25/12.54 tff(157,plain,
% 19.25/12.54 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(158,plain,
% 19.25/12.54 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[157])).
% 19.25/12.54 tff(159,plain,
% 19.25/12.54 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(160,plain,
% 19.25/12.54 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(161,plain,
% 19.25/12.54 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[160])).
% 19.25/12.54 tff(162,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 19.25/12.54 tff(163,plain,
% 19.25/12.54 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[162, 161])).
% 19.25/12.54 tff(164,plain,
% 19.25/12.54 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[163, 159])).
% 19.25/12.54 tff(165,plain,(
% 19.25/12.54 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(skolemize,[status(sab)],[164])).
% 19.25/12.54 tff(166,plain,
% 19.25/12.54 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[165, 158])).
% 19.25/12.54 tff(167,plain,
% 19.25/12.54 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(168,plain,
% 19.25/12.54 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 19.25/12.54 inference(quant_inst,[status(thm)],[])).
% 19.25/12.54 tff(169,plain,
% 19.25/12.54 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[168, 167])).
% 19.25/12.54 tff(170,plain,
% 19.25/12.54 (l1_struct_0(A!0)),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[169, 46, 166])).
% 19.25/12.54 tff(171,plain,
% 19.25/12.54 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(172,plain,
% 19.25/12.54 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[171])).
% 19.25/12.54 tff(173,plain,
% 19.25/12.54 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(174,plain,
% 19.25/12.54 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[173])).
% 19.25/12.54 tff(175,plain,
% 19.25/12.54 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(176,plain,
% 19.25/12.54 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(177,plain,
% 19.25/12.54 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[176])).
% 19.25/12.54 tff(178,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 19.25/12.54 tff(179,plain,
% 19.25/12.54 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[178, 177])).
% 19.25/12.54 tff(180,plain,
% 19.25/12.54 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[179, 175])).
% 19.25/12.54 tff(181,plain,(
% 19.25/12.54 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.25/12.54 inference(skolemize,[status(sab)],[180])).
% 19.25/12.54 tff(182,plain,
% 19.25/12.54 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[181, 174])).
% 19.25/12.54 tff(183,plain,
% 19.25/12.54 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[182, 172])).
% 19.25/12.54 tff(184,plain,
% 19.25/12.54 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(185,plain,
% 19.25/12.54 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(186,plain,
% 19.25/12.54 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 19.25/12.54 inference(monotonicity,[status(thm)],[185])).
% 19.25/12.54 tff(187,plain,
% 19.25/12.54 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 19.25/12.54 inference(transitivity,[status(thm)],[186, 184])).
% 19.25/12.54 tff(188,plain,
% 19.25/12.54 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 19.25/12.54 inference(quant_inst,[status(thm)],[])).
% 19.25/12.54 tff(189,plain,
% 19.25/12.54 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[188, 187])).
% 19.25/12.54 tff(190,plain,
% 19.25/12.54 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[189, 48, 183])).
% 19.25/12.54 tff(191,plain,
% 19.25/12.54 (~v1_xboole_0(u1_struct_0(A!0))),
% 19.25/12.54 inference(unit_resolution,[status(thm)],[190, 170])).
% 19.25/12.54 tff(192,plain,
% 19.25/12.54 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(193,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[192])).
% 19.25/12.54 tff(194,plain,
% 19.25/12.54 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(195,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[194])).
% 19.25/12.54 tff(196,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(197,plain,
% 19.25/12.54 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))))),
% 19.25/12.54 inference(bind,[status(th)],[])).
% 19.25/12.54 tff(198,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 19.25/12.54 inference(quant_intro,[status(thm)],[197])).
% 19.25/12.54 tff(199,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_funct_2')).
% 19.25/12.54 tff(200,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[199, 198])).
% 19.25/12.54 tff(201,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[200, 196])).
% 19.25/12.54 tff(202,plain,(
% 19.25/12.54 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 19.25/12.54 inference(skolemize,[status(sab)],[201])).
% 19.25/12.54 tff(203,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[202, 195])).
% 19.25/12.54 tff(204,plain,
% 19.25/12.54 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.54 inference(modus_ponens,[status(thm)],[203, 193])).
% 19.25/12.54 tff(205,plain,
% 19.25/12.54 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(206,plain,
% 19.25/12.54 ((m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 19.25/12.54 inference(rewrite,[status(thm)],[])).
% 19.25/12.54 tff(207,plain,
% 19.25/12.54 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))))),
% 19.25/12.54 inference(monotonicity,[status(thm)],[206])).
% 19.25/12.54 tff(208,plain,
% 19.25/12.54 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 19.25/12.55 inference(transitivity,[status(thm)],[207, 205])).
% 19.25/12.55 tff(209,plain,
% 19.25/12.55 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))))),
% 19.25/12.55 inference(quant_inst,[status(thm)],[])).
% 19.25/12.55 tff(210,plain,
% 19.25/12.55 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[209, 208])).
% 19.25/12.55 tff(211,plain,
% 19.25/12.55 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.55 inference(unit_resolution,[status(thm)],[210, 73, 72, 204, 191, 156, 144])).
% 19.25/12.55 tff(212,plain,
% 19.25/12.55 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(213,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[212])).
% 19.25/12.55 tff(214,plain,
% 19.25/12.55 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(215,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[214])).
% 19.25/12.55 tff(216,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(transitivity,[status(thm)],[215, 213])).
% 19.25/12.55 tff(217,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(218,plain,
% 19.25/12.55 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m2_tsp_1(B, A) => l1_pre_topc(B)) <=> (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), (![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)) <=> ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), ((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))), rewrite((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), ((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(219,plain,
% 19.25/12.55 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[218])).
% 19.25/12.55 tff(220,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_tsp_1')).
% 19.25/12.55 tff(221,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[220, 219])).
% 19.25/12.55 tff(222,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[221, 217])).
% 19.25/12.55 tff(223,plain,(
% 19.25/12.55 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(skolemize,[status(sab)],[222])).
% 19.25/12.55 tff(224,plain,
% 19.25/12.55 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[223, 216])).
% 19.25/12.55 tff(225,plain,
% 19.25/12.55 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | (~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(226,plain,
% 19.25/12.55 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))),
% 19.25/12.55 inference(quant_inst,[status(thm)],[])).
% 19.25/12.55 tff(227,plain,
% 19.25/12.55 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | (~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[226, 225])).
% 19.25/12.55 tff(228,plain,
% 19.25/12.55 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 19.25/12.55 inference(unit_resolution,[status(thm)],[227, 46, 224])).
% 19.25/12.55 tff(229,plain,
% 19.25/12.55 (((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))) <=> ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(230,plain,
% 19.25/12.55 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 19.25/12.55 inference(quant_inst,[status(thm)],[])).
% 19.25/12.55 tff(231,plain,
% 19.25/12.55 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[230, 229])).
% 19.25/12.55 tff(232,plain,
% 19.25/12.55 (l1_pre_topc(B!1)),
% 19.25/12.55 inference(unit_resolution,[status(thm)],[231, 56, 228])).
% 19.25/12.55 tff(233,plain,
% 19.25/12.55 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(234,plain,
% 19.25/12.55 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 19.25/12.55 inference(quant_inst,[status(thm)],[])).
% 19.25/12.55 tff(235,plain,
% 19.25/12.55 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[234, 233])).
% 19.25/12.55 tff(236,plain,
% 19.25/12.55 (l1_struct_0(B!1)),
% 19.25/12.55 inference(unit_resolution,[status(thm)],[235, 166, 232])).
% 19.25/12.55 tff(237,plain,
% 19.25/12.55 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(238,plain,
% 19.25/12.55 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[237])).
% 19.25/12.55 tff(239,plain,
% 19.25/12.55 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> ((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))))), rewrite(((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(240,plain,
% 19.25/12.55 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[239])).
% 19.25/12.55 tff(241,plain,
% 19.25/12.55 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(242,plain,
% 19.25/12.55 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(243,plain,
% 19.25/12.55 (![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[242])).
% 19.25/12.55 tff(244,axiom,(![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_struct_0')).
% 19.25/12.55 tff(245,plain,
% 19.25/12.55 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[244, 243])).
% 19.25/12.55 tff(246,plain,
% 19.25/12.55 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[245, 241])).
% 19.25/12.55 tff(247,plain,(
% 19.25/12.55 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 19.25/12.55 inference(skolemize,[status(sab)],[246])).
% 19.25/12.55 tff(248,plain,
% 19.25/12.55 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[247, 240])).
% 19.25/12.55 tff(249,plain,
% 19.25/12.55 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[248, 238])).
% 19.25/12.55 tff(250,plain,
% 19.25/12.55 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(251,plain,
% 19.25/12.55 ((v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1))) <=> (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(252,plain,
% 19.25/12.55 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))),
% 19.25/12.55 inference(monotonicity,[status(thm)],[251])).
% 19.25/12.55 tff(253,plain,
% 19.25/12.55 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.25/12.55 inference(transitivity,[status(thm)],[252, 250])).
% 19.25/12.55 tff(254,plain,
% 19.25/12.55 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1)))),
% 19.25/12.55 inference(quant_inst,[status(thm)],[])).
% 19.25/12.55 tff(255,plain,
% 19.25/12.55 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[254, 253])).
% 19.25/12.55 tff(256,plain,
% 19.25/12.55 ((~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.25/12.55 inference(unit_resolution,[status(thm)],[255, 58, 249, 236])).
% 19.25/12.55 tff(257,plain,
% 19.25/12.55 (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.25/12.55 inference(unit_resolution,[status(thm)],[256, 211])).
% 19.25/12.55 tff(258,plain,
% 19.25/12.55 (k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.25/12.55 inference(symmetry,[status(thm)],[257])).
% 19.25/12.55 tff(259,plain,
% 19.25/12.55 (^[A: $i, B: $i, C: $i, D: $i] : refl((v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(260,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[259])).
% 19.25/12.55 tff(261,plain,
% 19.25/12.55 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(262,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[261])).
% 19.25/12.55 tff(263,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(264,plain,
% 19.25/12.55 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 19.25/12.55 inference(bind,[status(th)],[])).
% 19.25/12.55 tff(265,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 19.25/12.55 inference(quant_intro,[status(thm)],[264])).
% 19.25/12.55 tff(266,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 19.25/12.55 tff(267,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[266, 265])).
% 19.25/12.55 tff(268,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[267, 263])).
% 19.25/12.55 tff(269,plain,(
% 19.25/12.55 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 19.25/12.55 inference(skolemize,[status(sab)],[268])).
% 19.25/12.55 tff(270,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[269, 262])).
% 19.25/12.55 tff(271,plain,
% 19.25/12.55 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 19.25/12.55 inference(modus_ponens,[status(thm)],[270, 260])).
% 19.25/12.55 tff(272,plain,
% 19.25/12.55 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(273,plain,
% 19.25/12.55 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.25/12.55 inference(rewrite,[status(thm)],[])).
% 19.25/12.55 tff(274,plain,
% 19.25/12.55 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.25/12.55 inference(monotonicity,[status(thm)],[273])).
% 19.25/12.55 tff(275,plain,
% 19.25/12.55 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.25/12.56 inference(transitivity,[status(thm)],[274, 272])).
% 19.25/12.56 tff(276,plain,
% 19.25/12.56 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))))),
% 19.25/12.56 inference(quant_inst,[status(thm)],[])).
% 19.25/12.56 tff(277,plain,
% 19.25/12.56 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[276, 275])).
% 19.25/12.56 tff(278,plain,
% 19.25/12.56 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[277, 73, 72, 271, 191, 156, 144])).
% 19.25/12.56 tff(279,plain,
% 19.25/12.56 (k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))),
% 19.25/12.56 inference(symmetry,[status(thm)],[278])).
% 19.25/12.56 tff(280,plain,
% 19.25/12.56 (k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.25/12.56 inference(monotonicity,[status(thm)],[279])).
% 19.25/12.56 tff(281,plain,
% 19.25/12.56 (m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) <=> m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.56 inference(monotonicity,[status(thm)],[279])).
% 19.25/12.56 tff(282,plain,
% 19.25/12.56 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) <=> m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.56 inference(symmetry,[status(thm)],[281])).
% 19.25/12.56 tff(283,plain,
% 19.25/12.56 (m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[211, 282])).
% 19.25/12.56 tff(284,plain,
% 19.25/12.56 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(285,plain,
% 19.25/12.56 ((v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1))) <=> (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(286,plain,
% 19.25/12.56 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))))),
% 19.25/12.56 inference(monotonicity,[status(thm)],[285])).
% 19.25/12.56 tff(287,plain,
% 19.25/12.56 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))),
% 19.25/12.56 inference(transitivity,[status(thm)],[286, 284])).
% 19.25/12.56 tff(288,plain,
% 19.25/12.56 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1)))),
% 19.25/12.56 inference(quant_inst,[status(thm)],[])).
% 19.25/12.56 tff(289,plain,
% 19.25/12.56 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[288, 287])).
% 19.25/12.56 tff(290,plain,
% 19.25/12.56 ((~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[289, 58, 183])).
% 19.25/12.56 tff(291,plain,
% 19.25/12.56 (~v1_xboole_0(u1_struct_0(B!1))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[290, 236])).
% 19.25/12.56 tff(292,plain,
% 19.25/12.56 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(293,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[292])).
% 19.25/12.56 tff(294,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(295,plain,
% 19.25/12.56 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(296,plain,
% 19.25/12.56 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[295])).
% 19.25/12.56 tff(297,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 19.25/12.56 tff(298,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[297, 296])).
% 19.25/12.56 tff(299,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[298, 294])).
% 19.25/12.56 tff(300,plain,(
% 19.25/12.56 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(skolemize,[status(sab)],[299])).
% 19.25/12.56 tff(301,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[300, 293])).
% 19.25/12.56 tff(302,plain,
% 19.25/12.56 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(303,plain,
% 19.25/12.56 ((r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))) <=> (v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(304,plain,
% 19.25/12.56 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))))),
% 19.25/12.56 inference(monotonicity,[status(thm)],[303])).
% 19.25/12.56 tff(305,plain,
% 19.25/12.56 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 19.25/12.56 inference(transitivity,[status(thm)],[304, 302])).
% 19.25/12.56 tff(306,plain,
% 19.25/12.56 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))))),
% 19.25/12.56 inference(quant_inst,[status(thm)],[])).
% 19.25/12.56 tff(307,plain,
% 19.25/12.56 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[306, 305])).
% 19.25/12.56 tff(308,plain,
% 19.25/12.56 ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[307, 301, 291])).
% 19.25/12.56 tff(309,plain,
% 19.25/12.56 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[308, 283])).
% 19.25/12.56 tff(310,plain,
% 19.25/12.56 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(311,plain,
% 19.25/12.56 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[310])).
% 19.25/12.56 tff(312,plain,
% 19.25/12.56 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(313,plain,
% 19.25/12.56 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[312])).
% 19.25/12.56 tff(314,plain,
% 19.25/12.56 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 19.25/12.56 inference(transitivity,[status(thm)],[313, 311])).
% 19.25/12.56 tff(315,plain,
% 19.25/12.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(316,plain,
% 19.25/12.56 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[315])).
% 19.25/12.56 tff(317,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(318,plain,
% 19.25/12.56 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(319,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[318])).
% 19.25/12.56 tff(320,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 19.25/12.56 tff(321,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[320, 319])).
% 19.25/12.56 tff(322,plain,
% 19.25/12.56 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[321, 317])).
% 19.25/12.56 tff(323,plain,(
% 19.25/12.56 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))),
% 19.25/12.56 inference(skolemize,[status(sab)],[322])).
% 19.25/12.56 tff(324,plain,
% 19.25/12.56 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[323, 316])).
% 19.25/12.56 tff(325,plain,
% 19.25/12.56 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[324, 314])).
% 19.25/12.56 tff(326,plain,
% 19.25/12.56 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~(r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)) | (~((~r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(B!1))) | r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(A!0))))))))),
% 19.25/12.56 inference(quant_inst,[status(thm)],[])).
% 19.25/12.56 tff(327,plain,
% 19.25/12.56 (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~(r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)) | (~((~r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(B!1))) | r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(A!0)))))))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[326, 325])).
% 19.25/12.56 tff(328,plain,
% 19.25/12.56 (((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~(r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)) | (~((~r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(B!1))) | r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(A!0))))))) | ((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))),
% 19.25/12.56 inference(tautology,[status(thm)],[])).
% 19.25/12.56 tff(329,plain,
% 19.25/12.56 ((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[328, 327])).
% 19.25/12.56 tff(330,plain,
% 19.25/12.56 (^[A: $i, B: $i] : refl((m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(331,plain,
% 19.25/12.56 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[330])).
% 19.25/12.56 tff(332,plain,
% 19.25/12.56 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(333,axiom,(![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 19.25/12.56 tff(334,plain,
% 19.25/12.56 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[333, 332])).
% 19.25/12.56 tff(335,plain,(
% 19.25/12.56 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.25/12.56 inference(skolemize,[status(sab)],[334])).
% 19.25/12.56 tff(336,plain,
% 19.25/12.56 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[335, 331])).
% 19.25/12.56 tff(337,plain,
% 19.25/12.56 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 19.25/12.56 inference(quant_inst,[status(thm)],[])).
% 19.25/12.56 tff(338,plain,
% 19.25/12.56 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[337, 336])).
% 19.25/12.56 tff(339,plain,
% 19.25/12.56 ((~(m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 19.25/12.56 inference(tautology,[status(thm)],[])).
% 19.25/12.56 tff(340,plain,
% 19.25/12.56 ((~(m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)))) | r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[339, 128])).
% 19.25/12.56 tff(341,plain,
% 19.25/12.56 (r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[340, 338])).
% 19.25/12.56 tff(342,plain,
% 19.25/12.56 ((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 19.25/12.56 inference(tautology,[status(thm)],[])).
% 19.25/12.56 tff(343,plain,
% 19.25/12.56 ((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[342, 341])).
% 19.25/12.56 tff(344,plain,
% 19.25/12.56 (![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[343, 329])).
% 19.25/12.56 tff(345,plain,
% 19.25/12.56 (((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(346,plain,
% 19.25/12.56 ((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 19.25/12.56 inference(quant_inst,[status(thm)],[])).
% 19.25/12.56 tff(347,plain,
% 19.25/12.56 ((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))),
% 19.25/12.56 inference(modus_ponens,[status(thm)],[346, 345])).
% 19.25/12.56 tff(348,plain,
% 19.25/12.56 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))),
% 19.25/12.56 inference(unit_resolution,[status(thm)],[347, 344, 309])).
% 19.25/12.56 tff(349,plain,
% 19.25/12.56 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.25/12.56 tff(350,plain,
% 19.25/12.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.25/12.56 inference(quant_intro,[status(thm)],[349])).
% 19.25/12.56 tff(351,plain,
% 19.25/12.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.25/12.56 inference(rewrite,[status(thm)],[])).
% 19.25/12.56 tff(352,plain,
% 19.25/12.56 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 19.25/12.56 inference(bind,[status(th)],[])).
% 19.32/12.56 tff(353,plain,
% 19.32/12.56 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.32/12.56 inference(quant_intro,[status(thm)],[352])).
% 19.32/12.56 tff(354,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 19.32/12.56 tff(355,plain,
% 19.32/12.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.32/12.56 inference(modus_ponens,[status(thm)],[354, 353])).
% 19.32/12.56 tff(356,plain,
% 19.32/12.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.32/12.56 inference(modus_ponens,[status(thm)],[355, 351])).
% 19.32/12.56 tff(357,plain,(
% 19.32/12.56 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.32/12.56 inference(skolemize,[status(sab)],[356])).
% 19.32/12.56 tff(358,plain,
% 19.32/12.56 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.32/12.56 inference(modus_ponens,[status(thm)],[357, 350])).
% 19.32/12.56 tff(359,plain,
% 19.32/12.56 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 19.32/12.56 inference(rewrite,[status(thm)],[])).
% 19.32/12.56 tff(360,plain,
% 19.32/12.56 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 19.32/12.56 inference(quant_inst,[status(thm)],[])).
% 19.32/12.56 tff(361,plain,
% 19.32/12.56 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))),
% 19.32/12.56 inference(modus_ponens,[status(thm)],[360, 359])).
% 19.32/12.56 tff(362,plain,
% 19.32/12.56 (m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))),
% 19.32/12.56 inference(unit_resolution,[status(thm)],[361, 358, 348])).
% 19.32/12.56 tff(363,plain,
% 19.32/12.56 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.56 inference(rewrite,[status(thm)],[])).
% 19.32/12.56 tff(364,plain,
% 19.32/12.56 ((v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.56 inference(rewrite,[status(thm)],[])).
% 19.32/12.56 tff(365,plain,
% 19.32/12.56 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))),
% 19.32/12.56 inference(monotonicity,[status(thm)],[364])).
% 19.32/12.56 tff(366,plain,
% 19.32/12.56 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.56 inference(transitivity,[status(thm)],[365, 363])).
% 19.32/12.56 tff(367,plain,
% 19.32/12.56 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 19.32/12.56 inference(quant_inst,[status(thm)],[])).
% 19.32/12.56 tff(368,plain,
% 19.32/12.56 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.56 inference(modus_ponens,[status(thm)],[367, 366])).
% 19.32/12.56 tff(369,plain,
% 19.32/12.56 (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.56 inference(unit_resolution,[status(thm)],[368, 48, 249, 170, 362])).
% 19.32/12.56 tff(370,plain,
% 19.32/12.56 (^[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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))))),
% 19.32/12.56 inference(bind,[status(th)],[])).
% 19.32/12.57 tff(371,plain,
% 19.32/12.57 (![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 19.32/12.57 inference(quant_intro,[status(thm)],[370])).
% 19.32/12.57 tff(372,plain,
% 19.32/12.57 (^[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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))))),
% 19.32/12.57 inference(bind,[status(th)],[])).
% 19.32/12.57 tff(373,plain,
% 19.32/12.57 (![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 19.32/12.57 inference(quant_intro,[status(thm)],[372])).
% 19.32/12.57 tff(374,plain,
% 19.32/12.57 (![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 19.32/12.57 inference(transitivity,[status(thm)],[373, 371])).
% 19.32/12.57 tff(375,plain,
% 19.32/12.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))))),
% 19.32/12.57 inference(bind,[status(th)],[])).
% 19.32/12.57 tff(376,plain,
% 19.32/12.57 (![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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), 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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 19.32/12.57 inference(quant_intro,[status(thm)],[375])).
% 19.32/12.57 tff(377,plain,
% 19.32/12.57 (![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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 19.32/12.57 inference(rewrite,[status(thm)],[])).
% 19.32/12.57 tff(378,plain,
% 19.32/12.57 (^[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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))) <=> (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))))) <=> (((~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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, 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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))))) <=> ((~((~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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))))),
% 19.32/12.57 inference(bind,[status(th)],[])).
% 19.32/12.57 tff(379,plain,
% 19.32/12.57 (![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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))))) <=> ![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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 19.32/12.57 inference(quant_intro,[status(thm)],[378])).
% 19.32/12.57 tff(380,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, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tsp_2')).
% 19.32/12.57 tff(381,plain,
% 19.32/12.57 (![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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 19.32/12.57 inference(modus_ponens,[status(thm)],[380, 379])).
% 19.32/12.57 tff(382,plain,
% 19.32/12.57 (![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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 19.32/12.57 inference(modus_ponens,[status(thm)],[381, 377])).
% 19.32/12.57 tff(383,plain,(
% 19.32/12.57 ![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] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))),
% 19.32/12.57 inference(skolemize,[status(sab)],[382])).
% 19.32/12.57 tff(384,plain,
% 19.32/12.57 (![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 19.32/12.57 inference(modus_ponens,[status(thm)],[383, 376])).
% 19.32/12.57 tff(385,plain,
% 19.32/12.57 (![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 19.32/12.57 inference(modus_ponens,[status(thm)],[384, 374])).
% 19.32/12.57 tff(386,plain,
% 19.32/12.57 (((~![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))),
% 19.32/12.57 inference(rewrite,[status(thm)],[])).
% 19.32/12.57 tff(387,plain,
% 19.32/12.57 ((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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) <=> (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)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))),
% 19.32/12.57 inference(rewrite,[status(thm)],[])).
% 19.32/12.57 tff(388,plain,
% 19.32/12.57 (((~![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))))),
% 19.32/12.57 inference(monotonicity,[status(thm)],[387])).
% 19.32/12.57 tff(389,plain,
% 19.32/12.57 (((~![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))),
% 19.32/12.57 inference(transitivity,[status(thm)],[388, 386])).
% 19.32/12.57 tff(390,plain,
% 19.32/12.57 ((~![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))),
% 19.32/12.57 inference(quant_inst,[status(thm)],[])).
% 19.32/12.57 tff(391,plain,
% 19.32/12.57 ((~![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)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(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)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))),
% 19.32/12.57 inference(modus_ponens,[status(thm)],[390, 389])).
% 19.32/12.57 tff(392,plain,
% 19.32/12.57 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))),
% 19.32/12.57 inference(unit_resolution,[status(thm)],[391, 48, 47, 46, 385])).
% 19.32/12.57 tff(393,plain,
% 19.32/12.57 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 19.32/12.57 inference(rewrite,[status(thm)],[])).
% 19.32/12.57 tff(394,plain,
% 19.32/12.57 (((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 19.32/12.57 inference(rewrite,[status(thm)],[])).
% 19.32/12.57 tff(395,plain,
% 19.32/12.57 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))))))),
% 19.32/12.57 inference(monotonicity,[status(thm)],[394])).
% 19.32/12.57 tff(396,plain,
% 19.32/12.57 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 19.32/12.58 inference(transitivity,[status(thm)],[395, 393])).
% 19.32/12.58 tff(397,plain,
% 19.32/12.58 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 19.32/12.58 inference(quant_inst,[status(thm)],[])).
% 19.32/12.58 tff(398,plain,
% 19.32/12.58 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[397, 396])).
% 19.32/12.58 tff(399,plain,
% 19.32/12.58 (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))),
% 19.32/12.58 inference(unit_resolution,[status(thm)],[398, 392, 128])).
% 19.32/12.58 tff(400,plain,
% 19.32/12.58 (((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))) | ((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))),
% 19.32/12.58 inference(tautology,[status(thm)],[])).
% 19.32/12.58 tff(401,plain,
% 19.32/12.58 ((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))),
% 19.32/12.58 inference(unit_resolution,[status(thm)],[400, 399])).
% 19.32/12.58 tff(402,plain,
% 19.32/12.58 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))))))))),
% 19.32/12.58 inference(bind,[status(th)],[])).
% 19.32/12.58 tff(403,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))),
% 19.32/12.58 inference(quant_intro,[status(thm)],[402])).
% 19.32/12.58 tff(404,plain,
% 19.32/12.58 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))))),
% 19.32/12.58 inference(bind,[status(th)],[])).
% 19.32/12.58 tff(405,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 19.32/12.58 inference(quant_intro,[status(thm)],[404])).
% 19.32/12.58 tff(406,plain,
% 19.32/12.58 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))))),
% 19.32/12.58 inference(bind,[status(th)],[])).
% 19.32/12.58 tff(407,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 19.32/12.58 inference(quant_intro,[status(thm)],[406])).
% 19.32/12.58 tff(408,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 19.32/12.58 inference(transitivity,[status(thm)],[407, 405])).
% 19.32/12.58 tff(409,plain,
% 19.32/12.58 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))))),
% 19.32/12.58 inference(bind,[status(th)],[])).
% 19.32/12.58 tff(410,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 19.32/12.58 inference(quant_intro,[status(thm)],[409])).
% 19.32/12.58 tff(411,plain,
% 19.32/12.58 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 19.32/12.58 inference(bind,[status(th)],[])).
% 19.32/12.58 tff(412,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))),
% 19.32/12.58 inference(quant_intro,[status(thm)],[411])).
% 19.32/12.58 tff(413,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 19.32/12.58 inference(rewrite,[status(thm)],[])).
% 19.32/12.58 tff(414,plain,
% 19.32/12.58 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))) <=> (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~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_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~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_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), ((l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), ((l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 19.32/12.58 inference(bind,[status(th)],[])).
% 19.32/12.58 tff(415,plain,
% 19.32/12.58 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 19.32/12.58 inference(quant_intro,[status(thm)],[414])).
% 19.32/12.58 tff(416,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_tsp_2')).
% 19.32/12.58 tff(417,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[416, 415])).
% 19.32/12.58 tff(418,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[417, 413])).
% 19.32/12.58 tff(419,plain,(
% 19.32/12.58 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 19.32/12.58 inference(skolemize,[status(sab)],[418])).
% 19.32/12.58 tff(420,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[419, 412])).
% 19.32/12.58 tff(421,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[420, 410])).
% 19.32/12.58 tff(422,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[421, 408])).
% 19.32/12.58 tff(423,plain,
% 19.32/12.58 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[422, 403])).
% 19.32/12.58 tff(424,plain,
% 19.32/12.58 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0))))))))))))),
% 19.32/12.58 inference(rewrite,[status(thm)],[])).
% 19.32/12.58 tff(425,plain,
% 19.32/12.58 (((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) <=> ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0))))))))))))),
% 19.32/12.58 inference(rewrite,[status(thm)],[])).
% 19.32/12.58 tff(426,plain,
% 19.32/12.58 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))))),
% 19.32/12.58 inference(monotonicity,[status(thm)],[425])).
% 19.32/12.58 tff(427,plain,
% 19.32/12.58 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0))))))))))))),
% 19.32/12.58 inference(transitivity,[status(thm)],[426, 424])).
% 19.32/12.58 tff(428,plain,
% 19.32/12.58 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))),
% 19.32/12.58 inference(quant_inst,[status(thm)],[])).
% 19.32/12.58 tff(429,plain,
% 19.32/12.58 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))),
% 19.32/12.58 inference(modus_ponens,[status(thm)],[428, 427])).
% 19.32/12.58 tff(430,plain,
% 19.32/12.58 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))),
% 19.32/12.58 inference(unit_resolution,[status(thm)],[429, 46, 423])).
% 19.32/12.58 tff(431,plain,
% 19.32/12.58 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))),
% 19.32/12.58 inference(rewrite,[status(thm)],[])).
% 19.32/12.58 tff(432,plain,
% 19.32/12.58 (((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0))))))))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))),
% 19.32/12.58 inference(rewrite,[status(thm)],[])).
% 19.32/12.58 tff(433,plain,
% 19.32/12.58 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))))))))),
% 19.32/12.59 inference(monotonicity,[status(thm)],[432])).
% 19.32/12.59 tff(434,plain,
% 19.32/12.59 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))),
% 19.32/12.59 inference(transitivity,[status(thm)],[433, 431])).
% 19.32/12.59 tff(435,plain,
% 19.32/12.59 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))),
% 19.32/12.59 inference(quant_inst,[status(thm)],[])).
% 19.32/12.59 tff(436,plain,
% 19.32/12.59 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[435, 434])).
% 19.32/12.59 tff(437,plain,
% 19.32/12.59 (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[436, 430, 128])).
% 19.32/12.59 tff(438,plain,
% 19.32/12.59 (((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))))) | ((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))),
% 19.32/12.59 inference(tautology,[status(thm)],[])).
% 19.32/12.59 tff(439,plain,
% 19.32/12.59 ((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[438, 437])).
% 19.32/12.59 tff(440,plain,
% 19.32/12.59 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))))),
% 19.32/12.59 inference(bind,[status(th)],[])).
% 19.32/12.59 tff(441,plain,
% 19.32/12.59 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(quant_intro,[status(thm)],[440])).
% 19.32/12.59 tff(442,plain,
% 19.32/12.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))))),
% 19.32/12.59 inference(bind,[status(th)],[])).
% 19.32/12.59 tff(443,plain,
% 19.32/12.59 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(quant_intro,[status(thm)],[442])).
% 19.32/12.59 tff(444,plain,
% 19.32/12.59 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(transitivity,[status(thm)],[443, 441])).
% 19.32/12.59 tff(445,plain,
% 19.32/12.59 (^[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] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))))),
% 19.32/12.59 inference(bind,[status(th)],[])).
% 19.32/12.59 tff(446,plain,
% 19.32/12.59 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(quant_intro,[status(thm)],[445])).
% 19.32/12.59 tff(447,plain,
% 19.32/12.59 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(448,plain,
% 19.32/12.59 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))) <=> ((~(C = u1_struct_0(B))) | (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~(C = u1_struct_0(B))) | (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~(C = u1_struct_0(B))) | (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))), ((m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))) <=> (m2_tsp_1(B, A) => ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))), rewrite((m2_tsp_1(B, A) => ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))) <=> ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))), ((m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))) <=> ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))))), (![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))) <=> ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))))),
% 19.32/12.59 inference(bind,[status(th)],[])).
% 19.32/12.59 tff(449,plain,
% 19.32/12.59 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(quant_intro,[status(thm)],[448])).
% 19.32/12.59 tff(450,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t11_tsp_2')).
% 19.32/12.59 tff(451,plain,
% 19.32/12.59 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[450, 449])).
% 19.32/12.59 tff(452,plain,
% 19.32/12.59 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[451, 447])).
% 19.32/12.59 tff(453,plain,(
% 19.32/12.59 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(skolemize,[status(sab)],[452])).
% 19.32/12.59 tff(454,plain,
% 19.32/12.59 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[453, 446])).
% 19.32/12.59 tff(455,plain,
% 19.32/12.59 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[454, 444])).
% 19.32/12.59 tff(456,plain,
% 19.32/12.59 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)))))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(457,plain,
% 19.32/12.59 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = u1_struct_0(B)))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)))))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(458,plain,
% 19.32/12.59 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = u1_struct_0(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))))),
% 19.32/12.59 inference(monotonicity,[status(thm)],[457])).
% 19.32/12.59 tff(459,plain,
% 19.32/12.59 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = u1_struct_0(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)))))),
% 19.32/12.59 inference(transitivity,[status(thm)],[458, 456])).
% 19.32/12.59 tff(460,plain,
% 19.32/12.59 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = u1_struct_0(B))))))),
% 19.32/12.59 inference(quant_inst,[status(thm)],[])).
% 19.32/12.59 tff(461,plain,
% 19.32/12.59 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[460, 459])).
% 19.32/12.59 tff(462,plain,
% 19.32/12.59 (![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[461, 48, 46, 455])).
% 19.32/12.59 tff(463,plain,
% 19.32/12.59 (((~![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))) | ((~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0))))) <=> ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0))))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(464,plain,
% 19.32/12.59 ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))) | ((~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0))))),
% 19.32/12.59 inference(quant_inst,[status(thm)],[])).
% 19.32/12.59 tff(465,plain,
% 19.32/12.59 ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B, A!0))))) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[464, 463])).
% 19.32/12.59 tff(466,plain,
% 19.32/12.59 (![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[465, 56, 462])).
% 19.32/12.59 tff(467,plain,
% 19.32/12.59 (((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))) <=> ((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(468,plain,
% 19.32/12.59 (($false | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(469,plain,
% 19.32/12.59 (((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) <=> ($false | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(monotonicity,[status(thm)],[135])).
% 19.32/12.59 tff(470,plain,
% 19.32/12.59 (((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(transitivity,[status(thm)],[469, 468])).
% 19.32/12.59 tff(471,plain,
% 19.32/12.59 (((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))) <=> ((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))))),
% 19.32/12.59 inference(monotonicity,[status(thm)],[470])).
% 19.32/12.59 tff(472,plain,
% 19.32/12.59 (((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))) <=> ((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(transitivity,[status(thm)],[471, 467])).
% 19.32/12.59 tff(473,plain,
% 19.32/12.59 ((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.32/12.59 inference(quant_inst,[status(thm)],[])).
% 19.32/12.59 tff(474,plain,
% 19.32/12.59 ((~![C: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[473, 472])).
% 19.32/12.59 tff(475,plain,
% 19.32/12.59 (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[474, 466, 128])).
% 19.32/12.59 tff(476,plain,
% 19.32/12.59 ((~(v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) | v1_tsp_2(u1_struct_0(B!1), A!0) | (~v2_tsp_2(B!1, A!0))),
% 19.32/12.59 inference(tautology,[status(thm)],[])).
% 19.32/12.59 tff(477,plain,
% 19.32/12.59 ((~(v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) | v1_tsp_2(u1_struct_0(B!1), A!0)),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[476, 57])).
% 19.32/12.59 tff(478,plain,
% 19.32/12.59 (v1_tsp_2(u1_struct_0(B!1), A!0)),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[477, 475])).
% 19.32/12.59 tff(479,plain,
% 19.32/12.59 ((~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))) | (~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))),
% 19.32/12.59 inference(tautology,[status(thm)],[])).
% 19.32/12.59 tff(480,plain,
% 19.32/12.59 (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[479, 478, 439])).
% 19.32/12.59 tff(481,plain,
% 19.32/12.59 (((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(C, A!0)) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))) | v1_tsp_1(u1_struct_0(B!1), A!0)),
% 19.32/12.59 inference(tautology,[status(thm)],[])).
% 19.32/12.59 tff(482,plain,
% 19.32/12.59 (v1_tsp_1(u1_struct_0(B!1), A!0)),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[481, 480])).
% 19.32/12.59 tff(483,plain,
% 19.32/12.59 ((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))),
% 19.32/12.59 inference(tautology,[status(thm)],[])).
% 19.32/12.59 tff(484,plain,
% 19.32/12.59 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[483, 482, 401])).
% 19.32/12.59 tff(485,plain,
% 19.32/12.59 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.59 inference(rewrite,[status(thm)],[])).
% 19.32/12.59 tff(486,plain,
% 19.32/12.59 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.59 inference(quant_inst,[status(thm)],[])).
% 19.32/12.59 tff(487,plain,
% 19.32/12.59 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.59 inference(modus_ponens,[status(thm)],[486, 485])).
% 19.32/12.59 tff(488,plain,
% 19.32/12.59 ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[487, 484, 309])).
% 19.32/12.59 tff(489,plain,
% 19.32/12.59 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.59 inference(unit_resolution,[status(thm)],[488, 362])).
% 19.32/12.59 tff(490,plain,
% 19.32/12.59 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 19.32/12.59 inference(bind,[status(th)],[])).
% 19.32/12.59 tff(491,plain,
% 19.32/12.59 (![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 19.32/12.59 inference(quant_intro,[status(thm)],[490])).
% 19.32/12.59 tff(492,plain,
% 19.32/12.59 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k4_tex_4(A, B) = k2_tex_4(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 19.32/12.59 inference(bind,[status(th)],[])).
% 19.32/12.59 tff(493,plain,
% 19.32/12.59 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 19.32/12.59 inference(quant_intro,[status(thm)],[492])).
% 19.32/12.59 tff(494,plain,
% 19.32/12.59 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(495,plain,
% 19.32/12.60 (^[A: $i, B: $i] : trans(monotonicity(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))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))))),
% 19.32/12.60 inference(bind,[status(th)],[])).
% 19.32/12.60 tff(496,plain,
% 19.32/12.60 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 19.32/12.60 inference(quant_intro,[status(thm)],[495])).
% 19.32/12.60 tff(497,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_tex_4')).
% 19.32/12.60 tff(498,plain,
% 19.32/12.60 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[497, 496])).
% 19.32/12.60 tff(499,plain,
% 19.32/12.60 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[498, 494])).
% 19.32/12.60 tff(500,plain,(
% 19.32/12.60 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 19.32/12.60 inference(skolemize,[status(sab)],[499])).
% 19.32/12.60 tff(501,plain,
% 19.32/12.60 (![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[500, 493])).
% 19.32/12.60 tff(502,plain,
% 19.32/12.60 (![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[501, 491])).
% 19.32/12.60 tff(503,plain,
% 19.32/12.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(504,plain,
% 19.32/12.60 ((v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(505,plain,
% 19.32/12.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))),
% 19.32/12.60 inference(monotonicity,[status(thm)],[504])).
% 19.32/12.60 tff(506,plain,
% 19.32/12.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.60 inference(transitivity,[status(thm)],[505, 503])).
% 19.32/12.60 tff(507,plain,
% 19.32/12.60 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 19.32/12.60 inference(quant_inst,[status(thm)],[])).
% 19.32/12.60 tff(508,plain,
% 19.32/12.60 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[507, 506])).
% 19.32/12.60 tff(509,plain,
% 19.32/12.60 (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(unit_resolution,[status(thm)],[508, 48, 47, 46, 502, 362])).
% 19.32/12.60 tff(510,plain,
% 19.32/12.60 (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(symmetry,[status(thm)],[509])).
% 19.32/12.60 tff(511,plain,
% 19.32/12.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(512,plain,
% 19.32/12.60 ((v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(513,plain,
% 19.32/12.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.60 inference(monotonicity,[status(thm)],[512])).
% 19.32/12.60 tff(514,plain,
% 19.32/12.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.60 inference(transitivity,[status(thm)],[513, 511])).
% 19.32/12.60 tff(515,plain,
% 19.32/12.60 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 19.32/12.60 inference(quant_inst,[status(thm)],[])).
% 19.32/12.60 tff(516,plain,
% 19.32/12.60 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[515, 514])).
% 19.32/12.60 tff(517,plain,
% 19.32/12.60 (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))),
% 19.32/12.60 inference(unit_resolution,[status(thm)],[516, 48, 47, 46, 502, 144])).
% 19.32/12.60 tff(518,plain,
% 19.32/12.60 (k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))),
% 19.32/12.60 inference(symmetry,[status(thm)],[517])).
% 19.32/12.60 tff(519,plain,
% 19.32/12.60 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(monotonicity,[status(thm)],[279, 518])).
% 19.32/12.60 tff(520,plain,
% 19.32/12.60 (r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(symmetry,[status(thm)],[519])).
% 19.32/12.60 tff(521,plain,
% 19.32/12.60 (^[D: $i] : refl(((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) <=> ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))))),
% 19.32/12.60 inference(bind,[status(th)],[])).
% 19.32/12.60 tff(522,plain,
% 19.32/12.60 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))),
% 19.32/12.60 inference(quant_intro,[status(thm)],[521])).
% 19.32/12.60 tff(523,plain,
% 19.32/12.60 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))),
% 19.32/12.60 inference(and_elim,[status(thm)],[45])).
% 19.32/12.60 tff(524,plain,
% 19.32/12.60 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[523, 522])).
% 19.32/12.60 tff(525,plain,
% 19.32/12.60 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | ((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(526,plain,
% 19.32/12.60 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | ((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.60 inference(quant_inst,[status(thm)],[])).
% 19.32/12.60 tff(527,plain,
% 19.32/12.60 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[526, 525])).
% 19.32/12.60 tff(528,plain,
% 19.32/12.60 (r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(unit_resolution,[status(thm)],[527, 524, 144])).
% 19.32/12.60 tff(529,plain,
% 19.32/12.60 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[528, 520])).
% 19.32/12.60 tff(530,plain,
% 19.32/12.60 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))),
% 19.32/12.60 inference(bind,[status(th)],[])).
% 19.32/12.60 tff(531,plain,
% 19.32/12.60 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(quant_intro,[status(thm)],[530])).
% 19.32/12.60 tff(532,plain,
% 19.32/12.60 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))),
% 19.32/12.60 inference(bind,[status(th)],[])).
% 19.32/12.60 tff(533,plain,
% 19.32/12.60 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(quant_intro,[status(thm)],[532])).
% 19.32/12.60 tff(534,plain,
% 19.32/12.60 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(transitivity,[status(thm)],[533, 531])).
% 19.32/12.60 tff(535,plain,
% 19.32/12.60 (^[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] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))))),
% 19.32/12.60 inference(bind,[status(th)],[])).
% 19.32/12.60 tff(536,plain,
% 19.32/12.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(quant_intro,[status(thm)],[535])).
% 19.32/12.60 tff(537,plain,
% 19.32/12.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(rewrite,[status(thm)],[])).
% 19.32/12.60 tff(538,plain,
% 19.32/12.60 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))))),
% 19.32/12.60 inference(bind,[status(th)],[])).
% 19.32/12.60 tff(539,plain,
% 19.32/12.60 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(quant_intro,[status(thm)],[538])).
% 19.32/12.60 tff(540,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_tex_4')).
% 19.32/12.60 tff(541,plain,
% 19.32/12.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[540, 539])).
% 19.32/12.60 tff(542,plain,
% 19.32/12.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[541, 537])).
% 19.32/12.60 tff(543,plain,(
% 19.32/12.60 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(skolemize,[status(sab)],[542])).
% 19.32/12.60 tff(544,plain,
% 19.32/12.60 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[543, 536])).
% 19.32/12.60 tff(545,plain,
% 19.32/12.60 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 19.32/12.60 inference(modus_ponens,[status(thm)],[544, 534])).
% 19.32/12.60 tff(546,plain,
% 19.32/12.60 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B))))))),
% 19.32/12.61 inference(rewrite,[status(thm)],[])).
% 19.32/12.61 tff(547,plain,
% 19.32/12.61 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B))))))),
% 19.32/12.61 inference(quant_inst,[status(thm)],[])).
% 19.32/12.61 tff(548,plain,
% 19.32/12.61 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))),
% 19.32/12.61 inference(modus_ponens,[status(thm)],[547, 546])).
% 19.32/12.61 tff(549,plain,
% 19.32/12.61 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))),
% 19.32/12.61 inference(unit_resolution,[status(thm)],[548, 48, 46, 545])).
% 19.32/12.61 tff(550,plain,
% 19.32/12.61 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | ((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))),
% 19.32/12.61 inference(rewrite,[status(thm)],[])).
% 19.32/12.61 tff(551,plain,
% 19.32/12.61 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | ((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))),
% 19.32/12.61 inference(quant_inst,[status(thm)],[])).
% 19.32/12.61 tff(552,plain,
% 19.32/12.61 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | (~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.61 inference(modus_ponens,[status(thm)],[551, 550])).
% 19.32/12.61 tff(553,plain,
% 19.32/12.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.61 inference(unit_resolution,[status(thm)],[552, 549, 144])).
% 19.32/12.61 tff(554,plain,
% 19.32/12.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.61 inference(rewrite,[status(thm)],[])).
% 19.32/12.61 tff(555,plain,
% 19.32/12.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.32/12.61 inference(quant_inst,[status(thm)],[])).
% 19.32/12.61 tff(556,plain,
% 19.32/12.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.61 inference(modus_ponens,[status(thm)],[555, 554])).
% 19.32/12.61 tff(557,plain,
% 19.32/12.61 ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.32/12.61 inference(unit_resolution,[status(thm)],[556, 553])).
% 19.32/12.61 tff(558,plain,
% 19.32/12.61 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.32/12.61 inference(unit_resolution,[status(thm)],[557, 362])).
% 19.32/12.61 tff(559,plain,
% 19.32/12.61 ((~(r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))) | (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.41/12.66 inference(tautology,[status(thm)],[])).
% 19.41/12.66 tff(560,plain,
% 19.41/12.66 (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))),
% 19.41/12.66 inference(unit_resolution,[status(thm)],[559, 558, 529])).
% 19.41/12.66 tff(561,plain,
% 19.41/12.66 (k2_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.41/12.66 inference(symmetry,[status(thm)],[560])).
% 19.41/12.66 tff(562,plain,
% 19.41/12.66 (k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)) = k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.41/12.66 inference(transitivity,[status(thm)],[517, 561, 510])).
% 19.41/12.66 tff(563,plain,
% 19.41/12.66 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.41/12.66 inference(monotonicity,[status(thm)],[562])).
% 19.41/12.66 tff(564,plain,
% 19.41/12.66 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))),
% 19.41/12.66 inference(transitivity,[status(thm)],[563, 489, 369, 280, 258])).
% 19.41/12.66 tff(565,plain,
% 19.41/12.66 (((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))) | (~(k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))),
% 19.41/12.66 inference(tautology,[status(thm)],[])).
% 19.41/12.66 tff(566,plain,
% 19.41/12.66 (~(k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))),
% 19.41/12.66 inference(unit_resolution,[status(thm)],[565, 142])).
% 19.41/12.66 tff(567,plain,
% 19.41/12.66 ($false),
% 19.41/12.66 inference(unit_resolution,[status(thm)],[566, 564])).
% 19.41/12.66 % SZS output end Proof
%------------------------------------------------------------------------------