TSTP Solution File: TOP032+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP032+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 01:55:56 EDT 2022
% Result : Theorem 19.51s 12.70s
% Output : Proof 19.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP032+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 10:39:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 19.51/12.70 % SZS status Theorem
% 19.51/12.70 % SZS output start Proof
% 19.51/12.70 tff(k1_struct_0_type, type, (
% 19.51/12.70 k1_struct_0: ( $i * $i ) > $i)).
% 19.51/12.70 tff(k8_funct_2_type, type, (
% 19.51/12.70 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 19.51/12.70 tff(tptp_fun_E_25_type, type, (
% 19.51/12.70 tptp_fun_E_25: ( $i * $i * $i * $i ) > $i)).
% 19.51/12.70 tff(tptp_fun_A_0_type, type, (
% 19.51/12.70 tptp_fun_A_0: $i)).
% 19.51/12.70 tff(tptp_fun_B_1_type, type, (
% 19.51/12.70 tptp_fun_B_1: $i)).
% 19.51/12.70 tff(tptp_fun_C_2_type, type, (
% 19.51/12.70 tptp_fun_C_2: $i)).
% 19.51/12.70 tff(u1_struct_0_type, type, (
% 19.51/12.70 u1_struct_0: $i > $i)).
% 19.51/12.70 tff(k5_subset_1_type, type, (
% 19.51/12.70 k5_subset_1: ( $i * $i * $i ) > $i)).
% 19.51/12.70 tff(k4_tex_4_type, type, (
% 19.51/12.70 k4_tex_4: ( $i * $i ) > $i)).
% 19.51/12.70 tff(k1_tarski_type, type, (
% 19.51/12.70 k1_tarski: $i > $i)).
% 19.51/12.70 tff(m1_subset_1_type, type, (
% 19.51/12.70 m1_subset_1: ( $i * $i ) > $o)).
% 19.51/12.70 tff(m2_relset_1_type, type, (
% 19.51/12.70 m2_relset_1: ( $i * $i * $i ) > $o)).
% 19.51/12.70 tff(v5_pre_topc_type, type, (
% 19.51/12.70 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 19.51/12.70 tff(v1_funct_2_type, type, (
% 19.51/12.70 v1_funct_2: ( $i * $i * $i ) > $o)).
% 19.51/12.70 tff(v1_funct_1_type, type, (
% 19.51/12.70 v1_funct_1: $i > $o)).
% 19.51/12.70 tff(r2_hidden_type, type, (
% 19.51/12.70 r2_hidden: ( $i * $i ) > $o)).
% 19.51/12.70 tff(m2_tsp_1_type, type, (
% 19.51/12.70 m2_tsp_1: ( $i * $i ) > $o)).
% 19.51/12.70 tff(v2_tsp_2_type, type, (
% 19.51/12.70 v2_tsp_2: ( $i * $i ) > $o)).
% 19.51/12.70 tff(v3_struct_0_type, type, (
% 19.51/12.70 v3_struct_0: $i > $o)).
% 19.51/12.70 tff(l1_pre_topc_type, type, (
% 19.51/12.70 l1_pre_topc: $i > $o)).
% 19.51/12.70 tff(v2_pre_topc_type, type, (
% 19.51/12.70 v2_pre_topc: $i > $o)).
% 19.51/12.70 tff(k1_zfmisc_1_type, type, (
% 19.51/12.70 k1_zfmisc_1: $i > $i)).
% 19.51/12.70 tff(m1_pre_topc_type, type, (
% 19.51/12.70 m1_pre_topc: ( $i * $i ) > $o)).
% 19.51/12.70 tff(m1_relset_1_type, type, (
% 19.51/12.70 m1_relset_1: ( $i * $i * $i ) > $o)).
% 19.51/12.70 tff(v1_xboole_0_type, type, (
% 19.51/12.70 v1_xboole_0: $i > $o)).
% 19.51/12.70 tff(l1_struct_0_type, type, (
% 19.51/12.70 l1_struct_0: $i > $o)).
% 19.51/12.70 tff(k1_funct_1_type, type, (
% 19.51/12.70 k1_funct_1: ( $i * $i ) > $i)).
% 19.51/12.70 tff(r1_tarski_type, type, (
% 19.51/12.70 r1_tarski: ( $i * $i ) > $o)).
% 19.51/12.70 tff(tptp_fun_C_4_type, type, (
% 19.51/12.70 tptp_fun_C_4: ( $i * $i ) > $i)).
% 19.51/12.70 tff(v1_tsp_1_type, type, (
% 19.51/12.70 v1_tsp_1: ( $i * $i ) > $o)).
% 19.51/12.70 tff(tptp_fun_C_3_type, type, (
% 19.51/12.70 tptp_fun_C_3: ( $i * $i ) > $i)).
% 19.51/12.70 tff(v1_tsp_2_type, type, (
% 19.51/12.70 v1_tsp_2: ( $i * $i ) > $o)).
% 19.51/12.70 tff(tptp_fun_C_5_type, type, (
% 19.51/12.70 tptp_fun_C_5: ( $i * $i ) > $i)).
% 19.51/12.70 tff(k2_tex_4_type, type, (
% 19.51/12.70 k2_tex_4: ( $i * $i ) > $i)).
% 19.51/12.70 tff(1,plain,
% 19.51/12.70 ((((~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) & (~(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, 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)) & 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) & (~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(2,plain,
% 19.51/12.70 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(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, 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)) & 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) & (~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(3,plain,
% 19.51/12.70 (((~(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, 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)) & 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)))) & ![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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(4,plain,
% 19.51/12.70 ((~(~(v1_funct_1(C!2) & v1_funct_2(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))))) <=> (v1_funct_1(C!2) & v1_funct_2(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)))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(5,plain,
% 19.51/12.70 (((~(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, 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)) & 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)))) & ![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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 19.51/12.70 inference(monotonicity,[status(thm)],[4])).
% 19.51/12.70 tff(6,plain,
% 19.51/12.70 (((~(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, 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)) & 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)))) & ![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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.51/12.70 inference(transitivity,[status(thm)],[5, 3])).
% 19.51/12.70 tff(7,plain,
% 19.51/12.70 ((~(~((~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))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(8,plain,
% 19.51/12.70 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(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, 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)) & 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)) & ((~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 19.51/12.70 inference(monotonicity,[status(thm)],[7, 6])).
% 19.51/12.70 tff(9,plain,
% 19.51/12.70 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(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, 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)) & 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) & (~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.51/12.70 inference(transitivity,[status(thm)],[8, 2])).
% 19.51/12.70 tff(10,plain,
% 19.51/12.70 ((~(~((~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))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(11,plain,
% 19.51/12.70 (((~(~((~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)))) & ((~(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, 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)) & 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) & (~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 19.51/12.70 inference(monotonicity,[status(thm)],[10, 9])).
% 19.51/12.70 tff(12,plain,
% 19.51/12.70 (((~(~((~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)))) & ((~(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, 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)) & 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) & (~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 19.51/12.70 inference(transitivity,[status(thm)],[11, 1])).
% 19.51/12.70 tff(13,plain,
% 19.51/12.70 ((~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(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] : ((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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 tff(14,plain,
% 19.51/12.70 ((~![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))) & 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))) => (((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] : ((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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 19.51/12.70 inference(rewrite,[status(thm)],[])).
% 19.51/12.70 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))) & 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))) => (((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)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_tsp_2')).
% 19.51/12.70 tff(16,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[15, 14])).
% 19.51/12.70 tff(17,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[16, 13])).
% 19.51/12.70 tff(18,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[17, 13])).
% 19.51/12.70 tff(19,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[18, 13])).
% 19.51/12.70 tff(20,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[19, 13])).
% 19.51/12.70 tff(21,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[20, 13])).
% 19.51/12.70 tff(22,plain,
% 19.51/12.70 (~![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)))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[21, 13])).
% 19.51/12.70 tff(23,plain,
% 19.51/12.70 ((~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) & (~(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, 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)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.51/12.70 inference(modus_ponens,[status(thm)],[22, 12])).
% 19.51/12.70 tff(24,plain,
% 19.51/12.70 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.51/12.70 inference(and_elim,[status(thm)],[23])).
% 19.51/12.70 tff(25,plain,
% 19.51/12.70 (v1_funct_1(C!2)),
% 19.51/12.71 inference(and_elim,[status(thm)],[23])).
% 19.51/12.71 tff(26,plain,
% 19.51/12.71 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.51/12.71 inference(and_elim,[status(thm)],[23])).
% 19.51/12.71 tff(27,plain,
% 19.51/12.71 ((~(~((~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))))),
% 19.51/12.71 inference(rewrite,[status(thm)],[])).
% 19.51/12.71 tff(28,plain,
% 19.51/12.71 ((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)))))),
% 19.51/12.71 inference(rewrite,[status(thm)],[])).
% 19.51/12.71 tff(29,plain,
% 19.51/12.71 ((~(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))))))),
% 19.51/12.71 inference(monotonicity,[status(thm)],[28])).
% 19.51/12.71 tff(30,plain,
% 19.51/12.71 ((~(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))))),
% 19.51/12.71 inference(transitivity,[status(thm)],[29, 27])).
% 19.51/12.71 tff(31,plain,
% 19.51/12.71 (~(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)))),
% 19.51/12.71 inference(and_elim,[status(thm)],[23])).
% 19.51/12.71 tff(32,plain,
% 19.51/12.71 ((~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)))),
% 19.51/12.71 inference(modus_ponens,[status(thm)],[31, 30])).
% 19.51/12.71 tff(33,plain,
% 19.51/12.71 (~v5_pre_topc(C!2, A!0, B!1)),
% 19.51/12.71 inference(unit_resolution,[status(thm)],[32, 26, 25, 24])).
% 19.51/12.71 tff(34,plain,
% 19.51/12.71 (((~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)))) | v5_pre_topc(C!2, A!0, B!1)),
% 19.51/12.71 inference(tautology,[status(thm)],[])).
% 19.51/12.71 tff(35,plain,
% 19.51/12.71 ((~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)))),
% 19.51/12.71 inference(unit_resolution,[status(thm)],[34, 33])).
% 19.51/12.71 tff(36,plain,
% 19.51/12.71 (^[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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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))) | (~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))) | (~((~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))))))))))),
% 19.51/12.71 inference(bind,[status(th)],[])).
% 19.51/12.71 tff(37,plain,
% 19.51/12.71 (![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))) | (~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))) | (~((~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))) | (~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))) | (~((~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)))))))))),
% 19.51/12.71 inference(quant_intro,[status(thm)],[36])).
% 19.51/12.71 tff(38,plain,
% 19.51/12.71 (^[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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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))) | (~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))) | (~((~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))))))))))),
% 19.51/12.71 inference(bind,[status(th)],[])).
% 19.51/12.71 tff(39,plain,
% 19.51/12.71 (![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))) | (~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))) | (~((~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))) | (~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))) | (~((~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)))))))))),
% 19.51/12.71 inference(quant_intro,[status(thm)],[38])).
% 19.51/12.71 tff(40,plain,
% 19.51/12.71 (![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))) | (~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))) | (~((~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))) | (~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))) | (~((~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)))))))))),
% 19.51/12.71 inference(transitivity,[status(thm)],[39, 37])).
% 19.51/12.71 tff(41,plain,
% 19.51/12.71 (^[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)) & 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))) | (~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)) & 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))) | (~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))) | (~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))) | (~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)) & 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))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), quant_intro(proof_bind(^[D: $i] : 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))) | (~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))))) | (~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))))) | (~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))))))) <=> ((~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))) | (~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))))))) <=> ((~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] : ((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))) | (~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] : ((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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))) | (~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))) | (~((~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((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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))) | (~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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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))) | (~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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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))) | (~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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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))) | (~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))) | (~((~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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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)))))))))))),
% 19.51/12.71 inference(bind,[status(th)],[])).
% 19.51/12.71 tff(42,plain,
% 19.51/12.71 (![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(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))) | (~((~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)))))))))),
% 19.51/12.71 inference(quant_intro,[status(thm)],[41])).
% 19.51/12.71 tff(43,plain,
% 19.51/12.71 (^[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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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)))))))))))),
% 19.51/12.71 inference(bind,[status(th)],[])).
% 19.51/12.71 tff(44,plain,
% 19.51/12.71 (![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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))))))))))),
% 19.51/12.71 inference(quant_intro,[status(thm)],[43])).
% 19.51/12.71 tff(45,plain,
% 19.51/12.71 (![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))))))))),
% 19.51/12.71 inference(rewrite,[status(thm)],[])).
% 19.51/12.71 tff(46,plain,
% 19.51/12.71 (^[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(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(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)) & 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)))))), 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))))), ((((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))))) => (((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 = 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))))) => (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((((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))))) => (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 = 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)))))) | (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 = 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))))) => (((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 = 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)))))) | (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)))))), ((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))))) => (((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))))) <=> (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)))))) | (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((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)))))) | (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 = 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))))) => (((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 = 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))))) => (((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] : ((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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))) & 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))))) => (((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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))))))))))),
% 19.51/12.71 inference(bind,[status(th)],[])).
% 19.51/12.71 tff(47,plain,
% 19.51/12.71 (![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))) & 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))))) => (((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] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))))))))),
% 19.51/12.71 inference(quant_intro,[status(thm)],[46])).
% 19.51/12.71 tff(48,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))) & 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))))) => (((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))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_tsp_2')).
% 19.51/12.71 tff(49,plain,
% 19.51/12.71 (![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))))))))),
% 19.51/12.71 inference(modus_ponens,[status(thm)],[48, 47])).
% 19.51/12.71 tff(50,plain,
% 19.51/12.71 (![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))))))))),
% 19.51/12.71 inference(modus_ponens,[status(thm)],[49, 45])).
% 19.51/12.71 tff(51,plain,(
% 19.51/12.71 ![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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 = 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))))))))),
% 19.51/12.71 inference(skolemize,[status(sab)],[50])).
% 19.51/12.71 tff(52,plain,
% 19.51/12.71 (![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)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $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))) | (~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))))))))))),
% 19.51/12.71 inference(modus_ponens,[status(thm)],[51, 44])).
% 19.51/12.71 tff(53,plain,
% 19.51/12.71 (![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))) | (~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))) | (~((~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)))))))))),
% 19.51/12.71 inference(modus_ponens,[status(thm)],[52, 42])).
% 19.51/12.71 tff(54,plain,
% 19.51/12.71 (![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))) | (~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))) | (~((~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)))))))))),
% 19.51/12.71 inference(modus_ponens,[status(thm)],[53, 40])).
% 19.51/12.71 tff(55,plain,
% 19.51/12.71 (l1_pre_topc(A!0)),
% 19.51/12.71 inference(and_elim,[status(thm)],[23])).
% 19.51/12.71 tff(56,plain,
% 19.51/12.71 (v2_pre_topc(A!0)),
% 19.51/12.71 inference(and_elim,[status(thm)],[23])).
% 19.51/12.71 tff(57,plain,
% 19.51/12.71 (~v3_struct_0(A!0)),
% 19.51/12.71 inference(and_elim,[status(thm)],[23])).
% 19.51/12.71 tff(58,plain,
% 19.51/12.71 (((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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)))))))))) <=> ((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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)))))))))),
% 19.51/12.72 inference(rewrite,[status(thm)],[])).
% 19.51/12.72 tff(59,plain,
% 19.51/12.72 ((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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~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)))))) | (~((~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))))))))) <=> (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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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)))))))))),
% 19.51/12.72 inference(rewrite,[status(thm)],[])).
% 19.51/12.72 tff(60,plain,
% 19.51/12.72 (((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~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)))))) | (~((~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)))))))))) <=> ((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))))),
% 19.51/12.72 inference(monotonicity,[status(thm)],[59])).
% 19.51/12.72 tff(61,plain,
% 19.51/12.72 (((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~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)))))) | (~((~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)))))))))) <=> ((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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)))))))))),
% 19.51/12.72 inference(transitivity,[status(thm)],[60, 58])).
% 19.51/12.72 tff(62,plain,
% 19.51/12.72 ((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~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)))))) | (~((~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)))))))))),
% 19.51/12.72 inference(quant_inst,[status(thm)],[])).
% 19.51/12.72 tff(63,plain,
% 19.51/12.72 ((~![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))) | (~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))) | (~((~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!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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))),
% 19.51/12.72 inference(modus_ponens,[status(thm)],[62, 61])).
% 19.51/12.72 tff(64,plain,
% 19.51/12.72 (![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))),
% 19.51/12.72 inference(unit_resolution,[status(thm)],[63, 57, 56, 55, 54])).
% 19.51/12.72 tff(65,plain,
% 19.51/12.72 (m2_tsp_1(B!1, A!0)),
% 19.51/12.72 inference(and_elim,[status(thm)],[23])).
% 19.51/12.72 tff(66,plain,
% 19.51/12.72 (v2_tsp_2(B!1, A!0)),
% 19.51/12.72 inference(and_elim,[status(thm)],[23])).
% 19.51/12.72 tff(67,plain,
% 19.51/12.72 (~v3_struct_0(B!1)),
% 19.51/12.72 inference(and_elim,[status(thm)],[23])).
% 19.51/12.72 tff(68,plain,
% 19.51/12.72 (((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | (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))) | (~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))) | (~((~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))))))))) <=> ((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | 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))) | (~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))) | (~((~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))))))))),
% 19.51/12.72 inference(rewrite,[status(thm)],[])).
% 19.51/12.72 tff(69,plain,
% 19.51/12.72 ((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))) | (~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))) | (~((~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)))))))) <=> (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))) | (~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))) | (~((~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))))))))),
% 19.51/12.72 inference(rewrite,[status(thm)],[])).
% 19.51/12.72 tff(70,plain,
% 19.51/12.72 (^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(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))))) <=> (~((~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 = u1_struct_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 = u1_struct_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)))))))), rewrite(((~(D = u1_struct_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)))))) <=> ((~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, 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 = u1_struct_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)))))) <=> ((~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, 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))) | (~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))) | (~((~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)))))))), (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~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))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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))))))))), rewrite(((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))), (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~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))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))))),
% 19.51/12.72 inference(bind,[status(th)],[])).
% 19.51/12.72 tff(71,plain,
% 19.51/12.72 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~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))))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))),
% 19.54/12.73 inference(quant_intro,[status(thm)],[70])).
% 19.54/12.73 tff(72,plain,
% 19.54/12.73 ((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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_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)))))))) <=> (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))) | (~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))) | (~((~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))))))))),
% 19.54/12.73 inference(monotonicity,[status(thm)],[71])).
% 19.54/12.73 tff(73,plain,
% 19.54/12.73 ((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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_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)))))))) <=> (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))) | (~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))) | (~((~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))))))))),
% 19.54/12.73 inference(transitivity,[status(thm)],[72, 69])).
% 19.54/12.73 tff(74,plain,
% 19.54/12.73 (((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | (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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_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))))))))) <=> ((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | (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))) | (~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))) | (~((~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)))))))))),
% 19.54/12.73 inference(monotonicity,[status(thm)],[73])).
% 19.54/12.73 tff(75,plain,
% 19.54/12.73 (((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | (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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_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))))))))) <=> ((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | 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))) | (~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))) | (~((~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))))))))),
% 19.54/12.73 inference(transitivity,[status(thm)],[74, 68])).
% 19.54/12.73 tff(76,plain,
% 19.54/12.73 ((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | (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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~(D = u1_struct_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))))))))),
% 19.54/12.73 inference(quant_inst,[status(thm)],[])).
% 19.54/12.73 tff(77,plain,
% 19.54/12.73 ((~![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))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~(D = u1_struct_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)))))) | (~((~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))))))))) | 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))) | (~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))) | (~((~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)))))))),
% 19.54/12.73 inference(modus_ponens,[status(thm)],[76, 75])).
% 19.54/12.73 tff(78,plain,
% 19.54/12.73 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))),
% 19.54/12.73 inference(unit_resolution,[status(thm)],[77, 67, 66, 65, 64])).
% 19.54/12.73 tff(79,plain,
% 19.54/12.73 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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))) | (~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))) | (~((~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)))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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))))))))),
% 19.54/12.73 inference(rewrite,[status(thm)],[])).
% 19.54/12.73 tff(80,plain,
% 19.54/12.73 (((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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)))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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))))))))),
% 19.54/12.73 inference(rewrite,[status(thm)],[])).
% 19.54/12.73 tff(81,plain,
% 19.54/12.73 (^[D: $i] : trans(monotonicity(rewrite((~((~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)))))), (((~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)))))) | (~((~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)))))) <=> ((~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)))))) | (~((~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)))))))), rewrite(((~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)))))) | (~((~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))))) | (~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)))))))), (((~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)))))) | (~((~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))))) | (~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)))))))))),
% 19.54/12.73 inference(bind,[status(th)],[])).
% 19.54/12.73 tff(82,plain,
% 19.54/12.73 (![D: $i] : ((~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)))))) | (~((~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] : ((~((~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))))) | (~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)))))))),
% 19.54/12.73 inference(quant_intro,[status(thm)],[81])).
% 19.54/12.73 tff(83,plain,
% 19.54/12.73 (((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~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)))))) | (~((~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))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~((~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))))) | (~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))))))))),
% 19.54/12.73 inference(monotonicity,[status(thm)],[82])).
% 19.54/12.73 tff(84,plain,
% 19.54/12.73 (((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~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)))))) | (~((~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))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~((~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))))) | (~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))))))))),
% 19.54/12.73 inference(transitivity,[status(thm)],[83, 80])).
% 19.54/12.73 tff(85,plain,
% 19.54/12.73 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~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)))))) | (~((~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)))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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)))))))))),
% 19.54/12.74 inference(monotonicity,[status(thm)],[84])).
% 19.54/12.74 tff(86,plain,
% 19.54/12.74 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~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)))))) | (~((~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)))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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))))))))),
% 19.54/12.74 inference(transitivity,[status(thm)],[85, 79])).
% 19.54/12.74 tff(87,plain,
% 19.54/12.74 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~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)))))) | (~((~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)))))))),
% 19.54/12.74 inference(quant_inst,[status(thm)],[])).
% 19.54/12.74 tff(88,plain,
% 19.54/12.74 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_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))) | (~((~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)))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(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))) | ![D: $i] : ((~((~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))))) | (~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)))))))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[87, 86])).
% 19.54/12.74 tff(89,plain,
% 19.54/12.74 (![D: $i] : ((~((~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))))) | (~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)))))))),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[88, 25, 26, 24, 78])).
% 19.54/12.74 tff(90,plain,
% 19.54/12.74 (^[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))))),
% 19.54/12.74 inference(bind,[status(th)],[])).
% 19.54/12.74 tff(91,plain,
% 19.54/12.74 (![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)))),
% 19.54/12.74 inference(quant_intro,[status(thm)],[90])).
% 19.54/12.74 tff(92,plain,
% 19.54/12.74 (^[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))))),
% 19.54/12.74 inference(bind,[status(th)],[])).
% 19.54/12.74 tff(93,plain,
% 19.54/12.74 (![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)))),
% 19.54/12.74 inference(quant_intro,[status(thm)],[92])).
% 19.54/12.74 tff(94,plain,
% 19.54/12.74 (![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)))),
% 19.54/12.74 inference(transitivity,[status(thm)],[93, 91])).
% 19.54/12.74 tff(95,plain,
% 19.54/12.74 (![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)))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(96,plain,
% 19.54/12.74 (^[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))))),
% 19.54/12.74 inference(bind,[status(th)],[])).
% 19.54/12.74 tff(97,plain,
% 19.54/12.74 (![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)))),
% 19.54/12.74 inference(quant_intro,[status(thm)],[96])).
% 19.54/12.74 tff(98,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_tsp_1')).
% 19.54/12.74 tff(99,plain,
% 19.54/12.74 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[98, 97])).
% 19.54/12.74 tff(100,plain,
% 19.54/12.74 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[99, 95])).
% 19.54/12.74 tff(101,plain,(
% 19.54/12.74 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.54/12.74 inference(skolemize,[status(sab)],[100])).
% 19.54/12.74 tff(102,plain,
% 19.54/12.74 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[101, 94])).
% 19.54/12.74 tff(103,plain,
% 19.54/12.74 (((~![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)))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(104,plain,
% 19.54/12.74 ((~![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)))),
% 19.54/12.74 inference(quant_inst,[status(thm)],[])).
% 19.54/12.74 tff(105,plain,
% 19.54/12.74 ((~![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))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[104, 103])).
% 19.54/12.74 tff(106,plain,
% 19.54/12.74 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[105, 55, 102])).
% 19.54/12.74 tff(107,plain,
% 19.54/12.74 ((~![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))),
% 19.54/12.74 inference(quant_inst,[status(thm)],[])).
% 19.54/12.74 tff(108,plain,
% 19.54/12.74 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[107, 106])).
% 19.54/12.74 tff(109,plain,
% 19.54/12.74 ((~(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)),
% 19.54/12.74 inference(tautology,[status(thm)],[])).
% 19.54/12.74 tff(110,plain,
% 19.54/12.74 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[109, 65])).
% 19.54/12.74 tff(111,plain,
% 19.54/12.74 (m1_pre_topc(B!1, A!0)),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[110, 108])).
% 19.54/12.74 tff(112,plain,
% 19.54/12.74 (^[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))))))),
% 19.54/12.74 inference(bind,[status(th)],[])).
% 19.54/12.74 tff(113,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(quant_intro,[status(thm)],[112])).
% 19.54/12.74 tff(114,plain,
% 19.54/12.74 (^[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))))))),
% 19.54/12.74 inference(bind,[status(th)],[])).
% 19.54/12.74 tff(115,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(quant_intro,[status(thm)],[114])).
% 19.54/12.74 tff(116,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(transitivity,[status(thm)],[115, 113])).
% 19.54/12.74 tff(117,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(118,plain,
% 19.54/12.74 (^[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)))))))),
% 19.54/12.74 inference(bind,[status(th)],[])).
% 19.54/12.74 tff(119,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(quant_intro,[status(thm)],[118])).
% 19.54/12.74 tff(120,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/sandbox2/benchmark/theBenchmark.p','t1_tsep_1')).
% 19.54/12.74 tff(121,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[120, 119])).
% 19.54/12.74 tff(122,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[121, 117])).
% 19.54/12.74 tff(123,plain,(
% 19.54/12.74 ![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)))))),
% 19.54/12.74 inference(skolemize,[status(sab)],[122])).
% 19.54/12.74 tff(124,plain,
% 19.54/12.74 (![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)))))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[123, 116])).
% 19.54/12.74 tff(125,plain,
% 19.54/12.74 (((~![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)))))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(126,plain,
% 19.54/12.74 ((~![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)))))),
% 19.54/12.74 inference(quant_inst,[status(thm)],[])).
% 19.54/12.74 tff(127,plain,
% 19.54/12.74 ((~![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))))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[126, 125])).
% 19.54/12.74 tff(128,plain,
% 19.54/12.74 (![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[127, 55, 124])).
% 19.54/12.74 tff(129,plain,
% 19.54/12.74 (((~![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))))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(130,plain,
% 19.54/12.74 ((~![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))))),
% 19.54/12.74 inference(quant_inst,[status(thm)],[])).
% 19.54/12.74 tff(131,plain,
% 19.54/12.74 ((~![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)))),
% 19.54/12.74 inference(modus_ponens,[status(thm)],[130, 129])).
% 19.54/12.74 tff(132,plain,
% 19.54/12.74 ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[131, 128])).
% 19.54/12.74 tff(133,plain,
% 19.54/12.74 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 19.54/12.74 inference(unit_resolution,[status(thm)],[132, 111])).
% 19.54/12.74 tff(134,plain,
% 19.54/12.74 (((~![D: $i] : ((~((~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))))) | (~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)))))))) | ((~((~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))))) | (~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] : ((~((~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))))) | (~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)))))))) | (~((~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))))) | (~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)))))))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(135,plain,
% 19.54/12.74 (((~((~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))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | $false | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))))))) <=> ((~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0)))))))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(136,plain,
% 19.54/12.74 ((~$true) <=> $false),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(137,plain,
% 19.54/12.74 ((u1_struct_0(B!1) = u1_struct_0(B!1)) <=> $true),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(138,plain,
% 19.54/12.74 ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) <=> (~$true)),
% 19.54/12.74 inference(monotonicity,[status(thm)],[137])).
% 19.54/12.74 tff(139,plain,
% 19.54/12.74 ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) <=> $false),
% 19.54/12.74 inference(transitivity,[status(thm)],[138, 136])).
% 19.54/12.74 tff(140,plain,
% 19.54/12.74 ((~((~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)))))),
% 19.54/12.74 inference(rewrite,[status(thm)],[])).
% 19.54/12.74 tff(141,plain,
% 19.54/12.74 (((~((~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))))) | (~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))))))) <=> ((~((~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))))) | (~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)))))))),
% 19.54/12.74 inference(monotonicity,[status(thm)],[140, 139])).
% 19.54/12.74 tff(142,plain,
% 19.54/12.74 (((~((~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))))) | (~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))))))) <=> ((~((~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))))) | (~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)))))))),
% 19.54/12.74 inference(transitivity,[status(thm)],[141, 135])).
% 19.54/12.74 tff(143,plain,
% 19.54/12.74 (((~![D: $i] : ((~((~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))))) | (~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)))))))) | ((~((~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))))) | (~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] : ((~((~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))))) | (~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)))))))) | ((~((~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))))) | (~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))))))))),
% 19.54/12.75 inference(monotonicity,[status(thm)],[142])).
% 19.54/12.75 tff(144,plain,
% 19.54/12.75 (((~![D: $i] : ((~((~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))))) | (~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)))))))) | ((~((~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))))) | (~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] : ((~((~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))))) | (~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)))))))) | (~((~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))))) | (~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)))))))),
% 19.54/12.75 inference(transitivity,[status(thm)],[143, 134])).
% 19.54/12.75 tff(145,plain,
% 19.54/12.75 ((~![D: $i] : ((~((~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))))) | (~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)))))))) | ((~((~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))))) | (~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)))))))),
% 19.54/12.75 inference(quant_inst,[status(thm)],[])).
% 19.54/12.75 tff(146,plain,
% 19.54/12.75 ((~![D: $i] : ((~((~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))))) | (~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)))))))) | (~((~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))))) | (~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))))))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[145, 144])).
% 19.54/12.75 tff(147,plain,
% 19.54/12.75 (~((~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)))))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[146, 133, 89, 35])).
% 19.54/12.75 tff(148,plain,
% 19.54/12.75 (((~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))),
% 19.54/12.75 inference(tautology,[status(thm)],[])).
% 19.54/12.75 tff(149,plain,
% 19.54/12.75 (m1_subset_1(tptp_fun_E_25(u1_struct_0(B!1), C!2, B!1, A!0), u1_struct_0(A!0))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[148, 147])).
% 19.54/12.75 tff(150,plain,
% 19.54/12.75 (^[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)))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(151,plain,
% 19.54/12.75 (![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))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[150])).
% 19.54/12.75 tff(152,plain,
% 19.54/12.75 (![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))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(153,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 19.54/12.75 tff(154,plain,
% 19.54/12.75 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[153, 152])).
% 19.54/12.75 tff(155,plain,(
% 19.54/12.75 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.54/12.75 inference(skolemize,[status(sab)],[154])).
% 19.54/12.75 tff(156,plain,
% 19.54/12.75 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[155, 151])).
% 19.54/12.75 tff(157,plain,
% 19.54/12.75 ((~![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)))),
% 19.54/12.75 inference(quant_inst,[status(thm)],[])).
% 19.54/12.75 tff(158,plain,
% 19.54/12.75 (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))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[157, 156])).
% 19.54/12.75 tff(159,plain,
% 19.54/12.75 ((~(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))),
% 19.54/12.75 inference(tautology,[status(thm)],[])).
% 19.54/12.75 tff(160,plain,
% 19.54/12.75 ((~(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))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[159, 24])).
% 19.54/12.75 tff(161,plain,
% 19.54/12.75 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[160, 158])).
% 19.54/12.75 tff(162,plain,
% 19.54/12.75 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(163,plain,
% 19.54/12.75 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[162])).
% 19.54/12.75 tff(164,plain,
% 19.54/12.75 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(165,plain,
% 19.54/12.75 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(166,plain,
% 19.54/12.75 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[165])).
% 19.54/12.75 tff(167,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 19.54/12.75 tff(168,plain,
% 19.54/12.75 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[167, 166])).
% 19.54/12.75 tff(169,plain,
% 19.54/12.75 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[168, 164])).
% 19.54/12.75 tff(170,plain,(
% 19.54/12.75 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(skolemize,[status(sab)],[169])).
% 19.54/12.75 tff(171,plain,
% 19.54/12.75 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[170, 163])).
% 19.54/12.75 tff(172,plain,
% 19.54/12.75 (((~![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)))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(173,plain,
% 19.54/12.75 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 19.54/12.75 inference(quant_inst,[status(thm)],[])).
% 19.54/12.75 tff(174,plain,
% 19.54/12.75 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[173, 172])).
% 19.54/12.75 tff(175,plain,
% 19.54/12.75 (l1_struct_0(A!0)),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[174, 55, 171])).
% 19.54/12.75 tff(176,plain,
% 19.54/12.75 (^[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))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(177,plain,
% 19.54/12.75 (![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)))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[176])).
% 19.54/12.75 tff(178,plain,
% 19.54/12.75 (^[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)))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(179,plain,
% 19.54/12.75 (![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)))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[178])).
% 19.54/12.75 tff(180,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(181,plain,
% 19.54/12.75 (^[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)))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(182,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[181])).
% 19.54/12.75 tff(183,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 19.54/12.75 tff(184,plain,
% 19.54/12.75 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[183, 182])).
% 19.54/12.75 tff(185,plain,
% 19.54/12.75 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[184, 180])).
% 19.54/12.75 tff(186,plain,(
% 19.54/12.75 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 19.54/12.75 inference(skolemize,[status(sab)],[185])).
% 19.54/12.75 tff(187,plain,
% 19.54/12.75 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[186, 179])).
% 19.54/12.75 tff(188,plain,
% 19.54/12.75 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[187, 177])).
% 19.54/12.75 tff(189,plain,
% 19.54/12.75 (((~![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))))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(190,plain,
% 19.54/12.75 ((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))))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(191,plain,
% 19.54/12.75 (((~![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)))))),
% 19.54/12.75 inference(monotonicity,[status(thm)],[190])).
% 19.54/12.75 tff(192,plain,
% 19.54/12.75 (((~![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))))),
% 19.54/12.75 inference(transitivity,[status(thm)],[191, 189])).
% 19.54/12.75 tff(193,plain,
% 19.54/12.75 ((~![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)))),
% 19.54/12.75 inference(quant_inst,[status(thm)],[])).
% 19.54/12.75 tff(194,plain,
% 19.54/12.75 ((~![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)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[193, 192])).
% 19.54/12.75 tff(195,plain,
% 19.54/12.75 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[194, 57, 188])).
% 19.54/12.75 tff(196,plain,
% 19.54/12.75 (~v1_xboole_0(u1_struct_0(A!0))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[195, 175])).
% 19.54/12.75 tff(197,plain,
% 19.54/12.75 (^[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))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(198,plain,
% 19.54/12.75 (![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)))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[197])).
% 19.54/12.75 tff(199,plain,
% 19.54/12.75 (^[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)))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(200,plain,
% 19.54/12.75 (![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)))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[199])).
% 19.54/12.75 tff(201,plain,
% 19.54/12.75 (![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))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(202,plain,
% 19.54/12.75 (^[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))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(203,plain,
% 19.54/12.75 (![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))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[202])).
% 19.54/12.75 tff(204,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/sandbox2/benchmark/theBenchmark.p','dt_k8_funct_2')).
% 19.54/12.75 tff(205,plain,
% 19.54/12.75 (![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))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[204, 203])).
% 19.54/12.75 tff(206,plain,
% 19.54/12.75 (![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))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[205, 201])).
% 19.54/12.75 tff(207,plain,(
% 19.54/12.75 ![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))),
% 19.54/12.75 inference(skolemize,[status(sab)],[206])).
% 19.54/12.75 tff(208,plain,
% 19.54/12.75 (![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)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[207, 200])).
% 19.54/12.75 tff(209,plain,
% 19.54/12.75 (![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)))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[208, 198])).
% 19.54/12.75 tff(210,plain,
% 19.54/12.75 (((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | 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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | 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)))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(211,plain,
% 19.54/12.75 ((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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | 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)))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(212,plain,
% 19.54/12.75 (((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | 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))))),
% 19.54/12.75 inference(monotonicity,[status(thm)],[211])).
% 19.54/12.75 tff(213,plain,
% 19.54/12.75 (((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | 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)))),
% 19.54/12.75 inference(transitivity,[status(thm)],[212, 210])).
% 19.54/12.75 tff(214,plain,
% 19.54/12.75 ((~![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))))),
% 19.54/12.75 inference(quant_inst,[status(thm)],[])).
% 19.54/12.75 tff(215,plain,
% 19.54/12.75 ((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | 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))),
% 19.54/12.75 inference(modus_ponens,[status(thm)],[214, 213])).
% 19.54/12.75 tff(216,plain,
% 19.54/12.75 (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))),
% 19.54/12.75 inference(unit_resolution,[status(thm)],[215, 25, 26, 209, 196, 161, 149])).
% 19.54/12.75 tff(217,plain,
% 19.54/12.75 (^[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)))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(218,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[217])).
% 19.54/12.75 tff(219,plain,
% 19.54/12.75 (^[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)))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(220,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[219])).
% 19.54/12.75 tff(221,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(transitivity,[status(thm)],[220, 218])).
% 19.54/12.75 tff(222,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(rewrite,[status(thm)],[])).
% 19.54/12.75 tff(223,plain,
% 19.54/12.75 (^[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))))))),
% 19.54/12.75 inference(bind,[status(th)],[])).
% 19.54/12.75 tff(224,plain,
% 19.54/12.75 (![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))))),
% 19.54/12.75 inference(quant_intro,[status(thm)],[223])).
% 19.54/12.75 tff(225,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_tsp_1')).
% 19.54/12.76 tff(226,plain,
% 19.54/12.76 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[225, 224])).
% 19.54/12.76 tff(227,plain,
% 19.54/12.76 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[226, 222])).
% 19.54/12.76 tff(228,plain,(
% 19.54/12.76 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.54/12.76 inference(skolemize,[status(sab)],[227])).
% 19.54/12.76 tff(229,plain,
% 19.54/12.76 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[228, 221])).
% 19.54/12.76 tff(230,plain,
% 19.54/12.76 (((~![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))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(231,plain,
% 19.54/12.76 ((~![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))))),
% 19.54/12.76 inference(quant_inst,[status(thm)],[])).
% 19.54/12.76 tff(232,plain,
% 19.54/12.76 ((~![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[231, 230])).
% 19.54/12.76 tff(233,plain,
% 19.54/12.76 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 19.54/12.76 inference(unit_resolution,[status(thm)],[232, 55, 229])).
% 19.54/12.76 tff(234,plain,
% 19.54/12.76 (((~![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)))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(235,plain,
% 19.54/12.76 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 19.54/12.76 inference(quant_inst,[status(thm)],[])).
% 19.54/12.76 tff(236,plain,
% 19.54/12.76 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[235, 234])).
% 19.54/12.76 tff(237,plain,
% 19.54/12.76 (l1_pre_topc(B!1)),
% 19.54/12.76 inference(unit_resolution,[status(thm)],[236, 65, 233])).
% 19.54/12.76 tff(238,plain,
% 19.54/12.76 (((~![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)))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(239,plain,
% 19.54/12.76 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 19.54/12.76 inference(quant_inst,[status(thm)],[])).
% 19.54/12.76 tff(240,plain,
% 19.54/12.76 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[239, 238])).
% 19.54/12.76 tff(241,plain,
% 19.54/12.76 (l1_struct_0(B!1)),
% 19.54/12.76 inference(unit_resolution,[status(thm)],[240, 171, 237])).
% 19.54/12.76 tff(242,plain,
% 19.54/12.76 (^[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))))),
% 19.54/12.76 inference(bind,[status(th)],[])).
% 19.54/12.76 tff(243,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(quant_intro,[status(thm)],[242])).
% 19.54/12.76 tff(244,plain,
% 19.54/12.76 (^[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)))))),
% 19.54/12.76 inference(bind,[status(th)],[])).
% 19.54/12.76 tff(245,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(quant_intro,[status(thm)],[244])).
% 19.54/12.76 tff(246,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(247,plain,
% 19.54/12.76 (^[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)))))),
% 19.54/12.76 inference(bind,[status(th)],[])).
% 19.54/12.76 tff(248,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(quant_intro,[status(thm)],[247])).
% 19.54/12.76 tff(249,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/sandbox2/benchmark/theBenchmark.p','redefinition_k1_struct_0')).
% 19.54/12.76 tff(250,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[249, 248])).
% 19.54/12.76 tff(251,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[250, 246])).
% 19.54/12.76 tff(252,plain,(
% 19.54/12.76 ![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)))),
% 19.54/12.76 inference(skolemize,[status(sab)],[251])).
% 19.54/12.76 tff(253,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[252, 245])).
% 19.54/12.76 tff(254,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[253, 243])).
% 19.54/12.76 tff(255,plain,
% 19.54/12.76 (((~![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)))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(256,plain,
% 19.54/12.76 ((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)))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(257,plain,
% 19.54/12.76 (((~![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))))))),
% 19.54/12.76 inference(monotonicity,[status(thm)],[256])).
% 19.54/12.76 tff(258,plain,
% 19.54/12.76 (((~![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)))))),
% 19.54/12.76 inference(transitivity,[status(thm)],[257, 255])).
% 19.54/12.76 tff(259,plain,
% 19.54/12.76 ((~![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)))),
% 19.54/12.76 inference(quant_inst,[status(thm)],[])).
% 19.54/12.76 tff(260,plain,
% 19.54/12.76 ((~![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))))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[259, 258])).
% 19.54/12.76 tff(261,plain,
% 19.54/12.76 ((~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))))),
% 19.54/12.76 inference(unit_resolution,[status(thm)],[260, 67, 254, 241])).
% 19.54/12.76 tff(262,plain,
% 19.54/12.76 (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)))),
% 19.54/12.76 inference(unit_resolution,[status(thm)],[261, 216])).
% 19.54/12.76 tff(263,plain,
% 19.54/12.76 (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)))),
% 19.54/12.76 inference(symmetry,[status(thm)],[262])).
% 19.54/12.76 tff(264,plain,
% 19.54/12.76 (^[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))))),
% 19.54/12.76 inference(bind,[status(th)],[])).
% 19.54/12.76 tff(265,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(quant_intro,[status(thm)],[264])).
% 19.54/12.76 tff(266,plain,
% 19.54/12.76 (^[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)))))),
% 19.54/12.76 inference(bind,[status(th)],[])).
% 19.54/12.76 tff(267,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(quant_intro,[status(thm)],[266])).
% 19.54/12.76 tff(268,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(269,plain,
% 19.54/12.76 (^[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)))))),
% 19.54/12.76 inference(bind,[status(th)],[])).
% 19.54/12.76 tff(270,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(quant_intro,[status(thm)],[269])).
% 19.54/12.76 tff(271,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/sandbox2/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 19.54/12.76 tff(272,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[271, 270])).
% 19.54/12.76 tff(273,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[272, 268])).
% 19.54/12.76 tff(274,plain,(
% 19.54/12.76 ![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)))),
% 19.54/12.76 inference(skolemize,[status(sab)],[273])).
% 19.54/12.76 tff(275,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[274, 267])).
% 19.54/12.76 tff(276,plain,
% 19.54/12.76 (![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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[275, 265])).
% 19.54/12.76 tff(277,plain,
% 19.54/12.76 (((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | (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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | (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))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(278,plain,
% 19.54/12.76 ((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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | (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))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(279,plain,
% 19.54/12.76 (((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | (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)))))),
% 19.54/12.76 inference(monotonicity,[status(thm)],[278])).
% 19.54/12.76 tff(280,plain,
% 19.54/12.76 (((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | (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))))),
% 19.54/12.76 inference(transitivity,[status(thm)],[279, 277])).
% 19.54/12.76 tff(281,plain,
% 19.54/12.76 ((~![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))))),
% 19.54/12.76 inference(quant_inst,[status(thm)],[])).
% 19.54/12.76 tff(282,plain,
% 19.54/12.76 ((~![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_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | v1_xboole_0(u1_struct_0(A!0)) | (~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))) | (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)))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[281, 280])).
% 19.54/12.76 tff(283,plain,
% 19.54/12.76 (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))),
% 19.54/12.76 inference(unit_resolution,[status(thm)],[282, 25, 26, 276, 196, 161, 149])).
% 19.54/12.76 tff(284,plain,
% 19.54/12.76 (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))),
% 19.54/12.76 inference(symmetry,[status(thm)],[283])).
% 19.54/12.76 tff(285,plain,
% 19.54/12.76 (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)))),
% 19.54/12.76 inference(monotonicity,[status(thm)],[284])).
% 19.54/12.76 tff(286,plain,
% 19.54/12.76 (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))),
% 19.54/12.76 inference(monotonicity,[status(thm)],[284])).
% 19.54/12.76 tff(287,plain,
% 19.54/12.76 (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))),
% 19.54/12.76 inference(symmetry,[status(thm)],[286])).
% 19.54/12.76 tff(288,plain,
% 19.54/12.76 (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))),
% 19.54/12.76 inference(modus_ponens,[status(thm)],[216, 287])).
% 19.54/12.76 tff(289,plain,
% 19.54/12.76 (((~![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))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(290,plain,
% 19.54/12.76 ((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))))),
% 19.54/12.76 inference(rewrite,[status(thm)],[])).
% 19.54/12.76 tff(291,plain,
% 19.54/12.76 (((~![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)))))),
% 19.54/12.76 inference(monotonicity,[status(thm)],[290])).
% 19.54/12.76 tff(292,plain,
% 19.54/12.76 (((~![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))))),
% 19.54/12.76 inference(transitivity,[status(thm)],[291, 289])).
% 19.54/12.76 tff(293,plain,
% 19.54/12.76 ((~![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)))),
% 19.54/12.76 inference(quant_inst,[status(thm)],[])).
% 19.54/12.76 tff(294,plain,
% 19.54/12.77 ((~![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)))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[293, 292])).
% 19.54/12.77 tff(295,plain,
% 19.54/12.77 ((~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[294, 67, 188])).
% 19.54/12.77 tff(296,plain,
% 19.54/12.77 (~v1_xboole_0(u1_struct_0(B!1))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[295, 241])).
% 19.54/12.77 tff(297,plain,
% 19.54/12.77 (^[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))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(298,plain,
% 19.54/12.77 (![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)))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[297])).
% 19.54/12.77 tff(299,plain,
% 19.54/12.77 (![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)))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(300,plain,
% 19.54/12.77 (^[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))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(301,plain,
% 19.54/12.77 (![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)))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[300])).
% 19.54/12.77 tff(302,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 19.54/12.77 tff(303,plain,
% 19.54/12.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[302, 301])).
% 19.54/12.77 tff(304,plain,
% 19.54/12.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[303, 299])).
% 19.54/12.77 tff(305,plain,(
% 19.54/12.77 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.54/12.77 inference(skolemize,[status(sab)],[304])).
% 19.54/12.77 tff(306,plain,
% 19.54/12.77 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[305, 298])).
% 19.54/12.77 tff(307,plain,
% 19.54/12.77 (((~![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)))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(308,plain,
% 19.54/12.77 ((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)))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(309,plain,
% 19.54/12.77 (((~![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))))),
% 19.54/12.77 inference(monotonicity,[status(thm)],[308])).
% 19.54/12.77 tff(310,plain,
% 19.54/12.77 (((~![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)))),
% 19.54/12.77 inference(transitivity,[status(thm)],[309, 307])).
% 19.54/12.77 tff(311,plain,
% 19.54/12.77 ((~![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))))),
% 19.54/12.77 inference(quant_inst,[status(thm)],[])).
% 19.54/12.77 tff(312,plain,
% 19.54/12.77 ((~![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))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[311, 310])).
% 19.54/12.77 tff(313,plain,
% 19.54/12.77 ((~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))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[312, 306, 296])).
% 19.54/12.77 tff(314,plain,
% 19.54/12.77 (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))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[313, 288])).
% 19.54/12.77 tff(315,plain,
% 19.54/12.77 (^[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))))))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(316,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[315])).
% 19.54/12.77 tff(317,plain,
% 19.54/12.77 (^[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))))))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(318,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[317])).
% 19.54/12.77 tff(319,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(transitivity,[status(thm)],[318, 316])).
% 19.54/12.77 tff(320,plain,
% 19.54/12.77 (^[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)))))))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(321,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[320])).
% 19.54/12.77 tff(322,plain,
% 19.54/12.77 (![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)))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(323,plain,
% 19.54/12.77 (^[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))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(324,plain,
% 19.54/12.77 (![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)))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[323])).
% 19.54/12.77 tff(325,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 19.54/12.77 tff(326,plain,
% 19.54/12.77 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[325, 324])).
% 19.54/12.77 tff(327,plain,
% 19.54/12.77 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[326, 322])).
% 19.54/12.77 tff(328,plain,(
% 19.54/12.77 ![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)))))),
% 19.54/12.77 inference(skolemize,[status(sab)],[327])).
% 19.54/12.77 tff(329,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[328, 321])).
% 19.54/12.77 tff(330,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[329, 319])).
% 19.54/12.77 tff(331,plain,
% 19.54/12.77 ((~![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))))))))),
% 19.54/12.77 inference(quant_inst,[status(thm)],[])).
% 19.54/12.77 tff(332,plain,
% 19.54/12.77 (~((~((~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)))))))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[331, 330])).
% 19.54/12.77 tff(333,plain,
% 19.54/12.77 (((~((~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))))),
% 19.54/12.77 inference(tautology,[status(thm)],[])).
% 19.54/12.77 tff(334,plain,
% 19.54/12.77 ((~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)))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[333, 332])).
% 19.54/12.77 tff(335,plain,
% 19.54/12.77 (^[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)))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(336,plain,
% 19.54/12.77 (![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))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[335])).
% 19.54/12.77 tff(337,plain,
% 19.54/12.77 (![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))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(338,axiom,(![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 19.54/12.77 tff(339,plain,
% 19.54/12.77 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[338, 337])).
% 19.54/12.77 tff(340,plain,(
% 19.54/12.77 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.54/12.77 inference(skolemize,[status(sab)],[339])).
% 19.54/12.77 tff(341,plain,
% 19.54/12.77 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[340, 336])).
% 19.54/12.77 tff(342,plain,
% 19.54/12.77 ((~![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)))),
% 19.54/12.77 inference(quant_inst,[status(thm)],[])).
% 19.54/12.77 tff(343,plain,
% 19.54/12.77 (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))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[342, 341])).
% 19.54/12.77 tff(344,plain,
% 19.54/12.77 ((~(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))),
% 19.54/12.77 inference(tautology,[status(thm)],[])).
% 19.54/12.77 tff(345,plain,
% 19.54/12.77 ((~(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))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[344, 133])).
% 19.54/12.77 tff(346,plain,
% 19.54/12.77 (r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[345, 343])).
% 19.54/12.77 tff(347,plain,
% 19.54/12.77 ((~((~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)))),
% 19.54/12.77 inference(tautology,[status(thm)],[])).
% 19.54/12.77 tff(348,plain,
% 19.54/12.77 ((~((~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)))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[347, 346])).
% 19.54/12.77 tff(349,plain,
% 19.54/12.77 (![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[348, 334])).
% 19.54/12.77 tff(350,plain,
% 19.54/12.77 (((~![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)))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(351,plain,
% 19.54/12.77 ((~![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)))),
% 19.54/12.77 inference(quant_inst,[status(thm)],[])).
% 19.54/12.77 tff(352,plain,
% 19.54/12.77 ((~![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))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[351, 350])).
% 19.54/12.77 tff(353,plain,
% 19.54/12.77 (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))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[352, 349, 314])).
% 19.54/12.77 tff(354,plain,
% 19.54/12.77 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(355,plain,
% 19.54/12.77 (![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))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[354])).
% 19.54/12.77 tff(356,plain,
% 19.54/12.77 (![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))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(357,plain,
% 19.54/12.77 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(358,plain,
% 19.54/12.77 (![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))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[357])).
% 19.54/12.77 tff(359,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 19.54/12.77 tff(360,plain,
% 19.54/12.77 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[359, 358])).
% 19.54/12.77 tff(361,plain,
% 19.54/12.77 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[360, 356])).
% 19.54/12.77 tff(362,plain,(
% 19.54/12.77 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.54/12.77 inference(skolemize,[status(sab)],[361])).
% 19.54/12.77 tff(363,plain,
% 19.54/12.77 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[362, 355])).
% 19.54/12.77 tff(364,plain,
% 19.54/12.77 (((~![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)))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(365,plain,
% 19.54/12.77 ((~![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)))),
% 19.54/12.77 inference(quant_inst,[status(thm)],[])).
% 19.54/12.77 tff(366,plain,
% 19.54/12.77 ((~![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))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[365, 364])).
% 19.54/12.77 tff(367,plain,
% 19.54/12.77 (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))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[366, 363, 353])).
% 19.54/12.77 tff(368,plain,
% 19.54/12.77 (((~![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)))))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(369,plain,
% 19.54/12.77 ((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)))))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(370,plain,
% 19.54/12.77 (((~![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))))))),
% 19.54/12.77 inference(monotonicity,[status(thm)],[369])).
% 19.54/12.77 tff(371,plain,
% 19.54/12.77 (((~![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)))))),
% 19.54/12.77 inference(transitivity,[status(thm)],[370, 368])).
% 19.54/12.77 tff(372,plain,
% 19.54/12.77 ((~![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)))),
% 19.54/12.77 inference(quant_inst,[status(thm)],[])).
% 19.54/12.77 tff(373,plain,
% 19.54/12.77 ((~![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))))),
% 19.54/12.77 inference(modus_ponens,[status(thm)],[372, 371])).
% 19.54/12.77 tff(374,plain,
% 19.54/12.77 (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)))),
% 19.54/12.77 inference(unit_resolution,[status(thm)],[373, 57, 254, 175, 367])).
% 19.54/12.77 tff(375,plain,
% 19.54/12.77 (^[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))))))))))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(376,plain,
% 19.54/12.77 (![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)))))))))))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[375])).
% 19.54/12.77 tff(377,plain,
% 19.54/12.77 (^[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))))))))))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(378,plain,
% 19.54/12.77 (![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)))))))))))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[377])).
% 19.54/12.77 tff(379,plain,
% 19.54/12.77 (![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)))))))))))),
% 19.54/12.77 inference(transitivity,[status(thm)],[378, 376])).
% 19.54/12.77 tff(380,plain,
% 19.54/12.77 (^[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)))))))))))))),
% 19.54/12.77 inference(bind,[status(th)],[])).
% 19.54/12.77 tff(381,plain,
% 19.54/12.77 (![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)))))))))))),
% 19.54/12.77 inference(quant_intro,[status(thm)],[380])).
% 19.54/12.77 tff(382,plain,
% 19.54/12.77 (![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)))))))),
% 19.54/12.77 inference(rewrite,[status(thm)],[])).
% 19.54/12.77 tff(383,plain,
% 19.54/12.77 (^[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)))))))))),
% 19.54/12.78 inference(bind,[status(th)],[])).
% 19.54/12.78 tff(384,plain,
% 19.54/12.78 (![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)))))))),
% 19.54/12.78 inference(quant_intro,[status(thm)],[383])).
% 19.54/12.78 tff(385,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/sandbox2/benchmark/theBenchmark.p','d2_tsp_2')).
% 19.54/12.78 tff(386,plain,
% 19.54/12.78 (![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)))))))),
% 19.54/12.78 inference(modus_ponens,[status(thm)],[385, 384])).
% 19.54/12.78 tff(387,plain,
% 19.54/12.78 (![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)))))))),
% 19.54/12.78 inference(modus_ponens,[status(thm)],[386, 382])).
% 19.54/12.78 tff(388,plain,(
% 19.54/12.78 ![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)))))))))),
% 19.54/12.78 inference(skolemize,[status(sab)],[387])).
% 19.54/12.78 tff(389,plain,
% 19.54/12.78 (![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)))))))))))),
% 19.54/12.78 inference(modus_ponens,[status(thm)],[388, 381])).
% 19.54/12.78 tff(390,plain,
% 19.54/12.78 (![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)))))))))))),
% 19.54/12.78 inference(modus_ponens,[status(thm)],[389, 379])).
% 19.54/12.78 tff(391,plain,
% 19.54/12.78 (((~![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)))))))))))),
% 19.54/12.78 inference(rewrite,[status(thm)],[])).
% 19.54/12.78 tff(392,plain,
% 19.54/12.78 ((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)))))))))))),
% 19.54/12.78 inference(rewrite,[status(thm)],[])).
% 19.54/12.78 tff(393,plain,
% 19.54/12.78 (((~![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))))))))))))),
% 19.54/12.78 inference(monotonicity,[status(thm)],[392])).
% 19.54/12.78 tff(394,plain,
% 19.54/12.78 (((~![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)))))))))))),
% 19.54/12.78 inference(transitivity,[status(thm)],[393, 391])).
% 19.54/12.78 tff(395,plain,
% 19.54/12.78 ((~![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)))))))))))),
% 19.54/12.78 inference(quant_inst,[status(thm)],[])).
% 19.54/12.78 tff(396,plain,
% 19.54/12.78 ((~![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))))))))))),
% 19.54/12.78 inference(modus_ponens,[status(thm)],[395, 394])).
% 19.54/12.78 tff(397,plain,
% 19.54/12.78 (![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))))))))))),
% 19.54/12.78 inference(unit_resolution,[status(thm)],[396, 57, 56, 55, 390])).
% 19.54/12.78 tff(398,plain,
% 19.54/12.78 (((~![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))))))))))),
% 19.54/12.78 inference(rewrite,[status(thm)],[])).
% 19.54/12.78 tff(399,plain,
% 19.54/12.78 (((~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))))))))))),
% 19.54/12.78 inference(rewrite,[status(thm)],[])).
% 19.54/12.78 tff(400,plain,
% 19.54/12.78 (((~![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)))))))))))),
% 19.54/12.78 inference(monotonicity,[status(thm)],[399])).
% 19.54/12.78 tff(401,plain,
% 19.54/12.78 (((~![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))))))))))),
% 19.54/12.78 inference(transitivity,[status(thm)],[400, 398])).
% 19.54/12.78 tff(402,plain,
% 19.54/12.78 ((~![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))))))))))),
% 19.54/12.78 inference(quant_inst,[status(thm)],[])).
% 19.54/12.78 tff(403,plain,
% 19.54/12.78 ((~![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)))))))))),
% 19.54/12.78 inference(modus_ponens,[status(thm)],[402, 401])).
% 19.54/12.78 tff(404,plain,
% 19.54/12.78 (~((~((~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))))))))),
% 19.54/12.78 inference(unit_resolution,[status(thm)],[403, 397, 133])).
% 19.54/12.78 tff(405,plain,
% 19.54/12.78 (((~((~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))))),
% 19.54/12.78 inference(tautology,[status(thm)],[])).
% 19.54/12.78 tff(406,plain,
% 19.54/12.78 ((~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)))),
% 19.54/12.78 inference(unit_resolution,[status(thm)],[405, 404])).
% 19.54/12.78 tff(407,plain,
% 19.54/12.78 (^[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)))))))))))))),
% 19.54/12.78 inference(bind,[status(th)],[])).
% 19.54/12.78 tff(408,plain,
% 19.54/12.78 (![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))))))))))))),
% 19.54/12.78 inference(quant_intro,[status(thm)],[407])).
% 19.54/12.78 tff(409,plain,
% 19.54/12.78 (^[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))))))))))))),
% 19.54/12.78 inference(bind,[status(th)],[])).
% 19.54/12.78 tff(410,plain,
% 19.54/12.78 (![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)))))))))))),
% 19.54/12.78 inference(quant_intro,[status(thm)],[409])).
% 19.54/12.78 tff(411,plain,
% 19.54/12.78 (^[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))))))))))))),
% 19.54/12.78 inference(bind,[status(th)],[])).
% 19.54/12.78 tff(412,plain,
% 19.54/12.78 (![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)))))))))))),
% 19.54/12.78 inference(quant_intro,[status(thm)],[411])).
% 19.54/12.79 tff(413,plain,
% 19.54/12.79 (![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)))))))))))),
% 19.54/12.79 inference(transitivity,[status(thm)],[412, 410])).
% 19.54/12.79 tff(414,plain,
% 19.54/12.79 (^[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))))))))))))),
% 19.54/12.79 inference(bind,[status(th)],[])).
% 19.54/12.79 tff(415,plain,
% 19.54/12.79 (![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)))))))))))),
% 19.54/12.79 inference(quant_intro,[status(thm)],[414])).
% 19.54/12.79 tff(416,plain,
% 19.54/12.79 (^[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)))))))))))),
% 19.54/12.79 inference(bind,[status(th)],[])).
% 19.54/12.79 tff(417,plain,
% 19.54/12.79 (![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))))))))))),
% 19.54/12.79 inference(quant_intro,[status(thm)],[416])).
% 19.54/12.79 tff(418,plain,
% 19.54/12.79 (![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)))))))))),
% 19.54/12.79 inference(rewrite,[status(thm)],[])).
% 19.54/12.79 tff(419,plain,
% 19.54/12.79 (^[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)))))))))))),
% 19.54/12.79 inference(bind,[status(th)],[])).
% 19.54/12.79 tff(420,plain,
% 19.54/12.79 (![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)))))))))),
% 19.54/12.79 inference(quant_intro,[status(thm)],[419])).
% 19.54/12.79 tff(421,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tsp_2')).
% 19.54/12.79 tff(422,plain,
% 19.54/12.79 (![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)))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[421, 420])).
% 19.54/12.79 tff(423,plain,
% 19.54/12.79 (![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)))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[422, 418])).
% 19.54/12.79 tff(424,plain,(
% 19.54/12.79 ![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)))))))))))),
% 19.54/12.79 inference(skolemize,[status(sab)],[423])).
% 19.54/12.79 tff(425,plain,
% 19.54/12.79 (![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))))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[424, 417])).
% 19.54/12.79 tff(426,plain,
% 19.54/12.79 (![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)))))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[425, 415])).
% 19.54/12.79 tff(427,plain,
% 19.54/12.79 (![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)))))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[426, 413])).
% 19.54/12.79 tff(428,plain,
% 19.54/12.79 (![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))))))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[427, 408])).
% 19.54/12.79 tff(429,plain,
% 19.54/12.79 (((~![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))))))))))))),
% 19.54/12.79 inference(rewrite,[status(thm)],[])).
% 19.54/12.79 tff(430,plain,
% 19.54/12.79 (((~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))))))))))))),
% 19.54/12.79 inference(rewrite,[status(thm)],[])).
% 19.54/12.79 tff(431,plain,
% 19.54/12.79 (((~![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)))))))))))))),
% 19.54/12.79 inference(monotonicity,[status(thm)],[430])).
% 19.54/12.79 tff(432,plain,
% 19.54/12.79 (((~![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))))))))))))),
% 19.54/12.79 inference(transitivity,[status(thm)],[431, 429])).
% 19.54/12.79 tff(433,plain,
% 19.54/12.79 ((~![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))))))))))))),
% 19.54/12.79 inference(quant_inst,[status(thm)],[])).
% 19.54/12.79 tff(434,plain,
% 19.54/12.79 ((~![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)))))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[433, 432])).
% 19.54/12.79 tff(435,plain,
% 19.54/12.79 (![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)))))))))))),
% 19.54/12.79 inference(unit_resolution,[status(thm)],[434, 55, 428])).
% 19.54/12.79 tff(436,plain,
% 19.54/12.79 (((~![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)))))))))))),
% 19.54/12.79 inference(rewrite,[status(thm)],[])).
% 19.54/12.79 tff(437,plain,
% 19.54/12.79 (((~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)))))))))))),
% 19.54/12.79 inference(rewrite,[status(thm)],[])).
% 19.54/12.79 tff(438,plain,
% 19.54/12.79 (((~![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))))))))))))),
% 19.54/12.79 inference(monotonicity,[status(thm)],[437])).
% 19.54/12.79 tff(439,plain,
% 19.54/12.79 (((~![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)))))))))))),
% 19.54/12.79 inference(transitivity,[status(thm)],[438, 436])).
% 19.54/12.79 tff(440,plain,
% 19.54/12.79 ((~![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)))))))))))),
% 19.54/12.79 inference(quant_inst,[status(thm)],[])).
% 19.54/12.79 tff(441,plain,
% 19.54/12.79 ((~![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))))))))))),
% 19.54/12.79 inference(modus_ponens,[status(thm)],[440, 439])).
% 19.54/12.79 tff(442,plain,
% 19.54/12.79 (~((~(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)))))))))),
% 19.54/12.79 inference(unit_resolution,[status(thm)],[441, 435, 133])).
% 19.54/12.79 tff(443,plain,
% 19.54/12.79 (((~(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)))))))),
% 19.54/12.79 inference(tautology,[status(thm)],[])).
% 19.54/12.79 tff(444,plain,
% 19.54/12.79 ((~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))))))),
% 19.54/12.79 inference(unit_resolution,[status(thm)],[443, 442])).
% 19.54/12.79 tff(445,plain,
% 19.54/12.79 (^[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)))))))),
% 19.54/12.79 inference(bind,[status(th)],[])).
% 19.54/12.79 tff(446,plain,
% 19.54/12.79 (![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))))))),
% 19.54/12.79 inference(quant_intro,[status(thm)],[445])).
% 19.54/12.79 tff(447,plain,
% 19.54/12.80 (^[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)))))))),
% 19.54/12.80 inference(bind,[status(th)],[])).
% 19.54/12.80 tff(448,plain,
% 19.54/12.80 (![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))))))),
% 19.54/12.80 inference(quant_intro,[status(thm)],[447])).
% 19.54/12.80 tff(449,plain,
% 19.54/12.80 (![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))))))),
% 19.54/12.80 inference(transitivity,[status(thm)],[448, 446])).
% 19.54/12.80 tff(450,plain,
% 19.54/12.80 (^[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))))))))),
% 19.54/12.80 inference(bind,[status(th)],[])).
% 19.54/12.80 tff(451,plain,
% 19.54/12.80 (![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))))))),
% 19.54/12.80 inference(quant_intro,[status(thm)],[450])).
% 19.54/12.80 tff(452,plain,
% 19.54/12.80 (![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))))))),
% 19.54/12.80 inference(rewrite,[status(thm)],[])).
% 19.54/12.80 tff(453,plain,
% 19.54/12.80 (^[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))))))))),
% 19.62/12.80 inference(bind,[status(th)],[])).
% 19.62/12.80 tff(454,plain,
% 19.62/12.80 (![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))))))),
% 19.62/12.80 inference(quant_intro,[status(thm)],[453])).
% 19.62/12.80 tff(455,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/sandbox2/benchmark/theBenchmark.p','t11_tsp_2')).
% 19.62/12.80 tff(456,plain,
% 19.62/12.80 (![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))))))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[455, 454])).
% 19.62/12.80 tff(457,plain,
% 19.62/12.80 (![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))))))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[456, 452])).
% 19.62/12.80 tff(458,plain,(
% 19.62/12.80 ![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))))))),
% 19.62/12.80 inference(skolemize,[status(sab)],[457])).
% 19.62/12.80 tff(459,plain,
% 19.62/12.80 (![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))))))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[458, 451])).
% 19.62/12.80 tff(460,plain,
% 19.62/12.80 (![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))))))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[459, 449])).
% 19.62/12.80 tff(461,plain,
% 19.62/12.80 (((~![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)))))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(462,plain,
% 19.62/12.80 ((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)))))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(463,plain,
% 19.62/12.80 (((~![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))))))),
% 19.62/12.80 inference(monotonicity,[status(thm)],[462])).
% 19.62/12.80 tff(464,plain,
% 19.62/12.80 (((~![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)))))),
% 19.62/12.80 inference(transitivity,[status(thm)],[463, 461])).
% 19.62/12.80 tff(465,plain,
% 19.62/12.80 ((~![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))))))),
% 19.62/12.80 inference(quant_inst,[status(thm)],[])).
% 19.62/12.80 tff(466,plain,
% 19.62/12.80 ((~![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))))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[465, 464])).
% 19.62/12.80 tff(467,plain,
% 19.62/12.80 (![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))))),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[466, 57, 55, 460])).
% 19.62/12.80 tff(468,plain,
% 19.62/12.80 (((~![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))))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(469,plain,
% 19.62/12.80 ((~![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))))),
% 19.62/12.80 inference(quant_inst,[status(thm)],[])).
% 19.62/12.80 tff(470,plain,
% 19.62/12.80 ((~![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)))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[469, 468])).
% 19.62/12.80 tff(471,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[470, 65, 467])).
% 19.62/12.80 tff(472,plain,
% 19.62/12.80 (((~![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: $i] : ((~(C = u1_struct_0(B!1))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(C, A!0) <=> v2_tsp_2(B!1, A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(473,plain,
% 19.62/12.80 (($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)))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(474,plain,
% 19.62/12.80 (((~(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)))),
% 19.62/12.80 inference(monotonicity,[status(thm)],[139])).
% 19.62/12.80 tff(475,plain,
% 19.62/12.80 (((~(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)))),
% 19.62/12.80 inference(transitivity,[status(thm)],[474, 473])).
% 19.62/12.80 tff(476,plain,
% 19.62/12.80 (((~![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))))),
% 19.62/12.80 inference(monotonicity,[status(thm)],[475])).
% 19.62/12.80 tff(477,plain,
% 19.62/12.80 (((~![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)))),
% 19.62/12.80 inference(transitivity,[status(thm)],[476, 472])).
% 19.62/12.80 tff(478,plain,
% 19.62/12.80 ((~![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)))),
% 19.62/12.80 inference(quant_inst,[status(thm)],[])).
% 19.62/12.80 tff(479,plain,
% 19.62/12.80 ((~![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))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[478, 477])).
% 19.62/12.80 tff(480,plain,
% 19.62/12.80 (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[479, 471, 133])).
% 19.62/12.80 tff(481,plain,
% 19.62/12.80 ((~(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))),
% 19.62/12.80 inference(tautology,[status(thm)],[])).
% 19.62/12.80 tff(482,plain,
% 19.62/12.80 ((~(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)),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[481, 66])).
% 19.62/12.80 tff(483,plain,
% 19.62/12.80 (v1_tsp_2(u1_struct_0(B!1), A!0)),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[482, 480])).
% 19.62/12.80 tff(484,plain,
% 19.62/12.80 ((~((~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))))))),
% 19.62/12.80 inference(tautology,[status(thm)],[])).
% 19.62/12.80 tff(485,plain,
% 19.62/12.80 (~((~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)))))),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[484, 483, 444])).
% 19.62/12.80 tff(486,plain,
% 19.62/12.80 (((~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)),
% 19.62/12.80 inference(tautology,[status(thm)],[])).
% 19.62/12.80 tff(487,plain,
% 19.62/12.80 (v1_tsp_1(u1_struct_0(B!1), A!0)),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[486, 485])).
% 19.62/12.80 tff(488,plain,
% 19.62/12.80 ((~((~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)))),
% 19.62/12.80 inference(tautology,[status(thm)],[])).
% 19.62/12.80 tff(489,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[488, 487, 406])).
% 19.62/12.80 tff(490,plain,
% 19.62/12.80 (((~![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)))))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(491,plain,
% 19.62/12.80 ((~![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)))))),
% 19.62/12.80 inference(quant_inst,[status(thm)],[])).
% 19.62/12.80 tff(492,plain,
% 19.62/12.80 ((~![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))))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[491, 490])).
% 19.62/12.80 tff(493,plain,
% 19.62/12.80 ((~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))))),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[492, 489, 314])).
% 19.62/12.80 tff(494,plain,
% 19.62/12.80 (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)))),
% 19.62/12.80 inference(unit_resolution,[status(thm)],[493, 367])).
% 19.62/12.80 tff(495,plain,
% 19.62/12.80 (^[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))))),
% 19.62/12.80 inference(bind,[status(th)],[])).
% 19.62/12.80 tff(496,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(quant_intro,[status(thm)],[495])).
% 19.62/12.80 tff(497,plain,
% 19.62/12.80 (^[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)))))),
% 19.62/12.80 inference(bind,[status(th)],[])).
% 19.62/12.80 tff(498,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(quant_intro,[status(thm)],[497])).
% 19.62/12.80 tff(499,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(500,plain,
% 19.62/12.80 (^[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)))))),
% 19.62/12.80 inference(bind,[status(th)],[])).
% 19.62/12.80 tff(501,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(quant_intro,[status(thm)],[500])).
% 19.62/12.80 tff(502,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/sandbox2/benchmark/theBenchmark.p','redefinition_k4_tex_4')).
% 19.62/12.80 tff(503,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[502, 501])).
% 19.62/12.80 tff(504,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[503, 499])).
% 19.62/12.80 tff(505,plain,(
% 19.62/12.80 ![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)))),
% 19.62/12.80 inference(skolemize,[status(sab)],[504])).
% 19.62/12.80 tff(506,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[505, 498])).
% 19.62/12.80 tff(507,plain,
% 19.62/12.80 (![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)))),
% 19.62/12.80 inference(modus_ponens,[status(thm)],[506, 496])).
% 19.62/12.80 tff(508,plain,
% 19.62/12.80 (((~![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)))))),
% 19.62/12.80 inference(rewrite,[status(thm)],[])).
% 19.62/12.80 tff(509,plain,
% 19.62/12.80 ((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)))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(510,plain,
% 19.62/12.81 (((~![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))))))),
% 19.62/12.81 inference(monotonicity,[status(thm)],[509])).
% 19.62/12.81 tff(511,plain,
% 19.62/12.81 (((~![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)))))),
% 19.62/12.81 inference(transitivity,[status(thm)],[510, 508])).
% 19.62/12.81 tff(512,plain,
% 19.62/12.81 ((~![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)))),
% 19.62/12.81 inference(quant_inst,[status(thm)],[])).
% 19.62/12.81 tff(513,plain,
% 19.62/12.81 ((~![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))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[512, 511])).
% 19.62/12.81 tff(514,plain,
% 19.62/12.81 (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)))),
% 19.62/12.81 inference(unit_resolution,[status(thm)],[513, 57, 56, 55, 507, 367])).
% 19.62/12.81 tff(515,plain,
% 19.62/12.81 (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)))),
% 19.62/12.81 inference(symmetry,[status(thm)],[514])).
% 19.62/12.81 tff(516,plain,
% 19.62/12.81 (((~![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))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(517,plain,
% 19.62/12.81 ((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))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(518,plain,
% 19.62/12.81 (((~![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)))))),
% 19.62/12.81 inference(monotonicity,[status(thm)],[517])).
% 19.62/12.81 tff(519,plain,
% 19.62/12.81 (((~![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))))),
% 19.62/12.81 inference(transitivity,[status(thm)],[518, 516])).
% 19.62/12.81 tff(520,plain,
% 19.62/12.81 ((~![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)))),
% 19.62/12.81 inference(quant_inst,[status(thm)],[])).
% 19.62/12.81 tff(521,plain,
% 19.62/12.81 ((~![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)))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[520, 519])).
% 19.62/12.81 tff(522,plain,
% 19.62/12.81 (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))),
% 19.62/12.81 inference(unit_resolution,[status(thm)],[521, 57, 56, 55, 507, 149])).
% 19.62/12.81 tff(523,plain,
% 19.62/12.81 (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))),
% 19.62/12.81 inference(symmetry,[status(thm)],[522])).
% 19.62/12.81 tff(524,plain,
% 19.62/12.81 (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)))),
% 19.62/12.81 inference(monotonicity,[status(thm)],[284, 523])).
% 19.62/12.81 tff(525,plain,
% 19.62/12.81 (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)))),
% 19.62/12.81 inference(symmetry,[status(thm)],[524])).
% 19.62/12.81 tff(526,plain,
% 19.62/12.81 (^[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))))),
% 19.62/12.81 inference(bind,[status(th)],[])).
% 19.62/12.81 tff(527,plain,
% 19.62/12.81 (![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)))),
% 19.62/12.81 inference(quant_intro,[status(thm)],[526])).
% 19.62/12.81 tff(528,plain,
% 19.62/12.81 (![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)))),
% 19.62/12.81 inference(and_elim,[status(thm)],[23])).
% 19.62/12.81 tff(529,plain,
% 19.62/12.81 (![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)))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[528, 527])).
% 19.62/12.81 tff(530,plain,
% 19.62/12.81 (((~![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))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(531,plain,
% 19.62/12.81 ((~![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))))),
% 19.62/12.81 inference(quant_inst,[status(thm)],[])).
% 19.62/12.81 tff(532,plain,
% 19.62/12.81 ((~![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)))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[531, 530])).
% 19.62/12.81 tff(533,plain,
% 19.62/12.81 (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)))),
% 19.62/12.81 inference(unit_resolution,[status(thm)],[532, 529, 149])).
% 19.62/12.81 tff(534,plain,
% 19.62/12.81 (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)))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[533, 525])).
% 19.62/12.81 tff(535,plain,
% 19.62/12.81 (^[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)))))))),
% 19.62/12.81 inference(bind,[status(th)],[])).
% 19.62/12.81 tff(536,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(quant_intro,[status(thm)],[535])).
% 19.62/12.81 tff(537,plain,
% 19.62/12.81 (^[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)))))))),
% 19.62/12.81 inference(bind,[status(th)],[])).
% 19.62/12.81 tff(538,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(quant_intro,[status(thm)],[537])).
% 19.62/12.81 tff(539,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(transitivity,[status(thm)],[538, 536])).
% 19.62/12.81 tff(540,plain,
% 19.62/12.81 (^[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))))))))),
% 19.62/12.81 inference(bind,[status(th)],[])).
% 19.62/12.81 tff(541,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(quant_intro,[status(thm)],[540])).
% 19.62/12.81 tff(542,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(543,plain,
% 19.62/12.81 (^[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))))))))),
% 19.62/12.81 inference(bind,[status(th)],[])).
% 19.62/12.81 tff(544,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(quant_intro,[status(thm)],[543])).
% 19.62/12.81 tff(545,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/sandbox2/benchmark/theBenchmark.p','t23_tex_4')).
% 19.62/12.81 tff(546,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[545, 544])).
% 19.62/12.81 tff(547,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[546, 542])).
% 19.62/12.81 tff(548,plain,(
% 19.62/12.81 ![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))))))),
% 19.62/12.81 inference(skolemize,[status(sab)],[547])).
% 19.62/12.81 tff(549,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[548, 541])).
% 19.62/12.81 tff(550,plain,
% 19.62/12.81 (![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))))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[549, 539])).
% 19.62/12.81 tff(551,plain,
% 19.62/12.81 (((~![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))))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(552,plain,
% 19.62/12.81 ((~![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))))))),
% 19.62/12.81 inference(quant_inst,[status(thm)],[])).
% 19.62/12.81 tff(553,plain,
% 19.62/12.81 ((~![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)))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[552, 551])).
% 19.62/12.81 tff(554,plain,
% 19.62/12.81 (![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)))))),
% 19.62/12.81 inference(unit_resolution,[status(thm)],[553, 57, 55, 550])).
% 19.62/12.81 tff(555,plain,
% 19.62/12.81 (((~![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))))))),
% 19.62/12.81 inference(rewrite,[status(thm)],[])).
% 19.62/12.81 tff(556,plain,
% 19.62/12.81 ((~![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))))))),
% 19.62/12.81 inference(quant_inst,[status(thm)],[])).
% 19.62/12.81 tff(557,plain,
% 19.62/12.81 ((~![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)))))),
% 19.62/12.81 inference(modus_ponens,[status(thm)],[556, 555])).
% 19.62/12.81 tff(558,plain,
% 19.62/12.81 (![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)))))),
% 19.62/12.81 inference(unit_resolution,[status(thm)],[557, 554, 149])).
% 19.62/12.81 tff(559,plain,
% 19.62/12.81 (((~![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)))))),
% 19.62/12.82 inference(rewrite,[status(thm)],[])).
% 19.62/12.82 tff(560,plain,
% 19.62/12.82 ((~![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)))))),
% 19.62/12.82 inference(quant_inst,[status(thm)],[])).
% 19.62/12.82 tff(561,plain,
% 19.62/12.82 ((~![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))))),
% 19.62/12.82 inference(modus_ponens,[status(thm)],[560, 559])).
% 19.62/12.82 tff(562,plain,
% 19.62/12.82 ((~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))))),
% 19.62/12.82 inference(unit_resolution,[status(thm)],[561, 558])).
% 19.62/12.82 tff(563,plain,
% 19.62/12.82 (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)))),
% 19.62/12.82 inference(unit_resolution,[status(thm)],[562, 367])).
% 19.62/12.82 tff(564,plain,
% 19.62/12.82 ((~(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)))),
% 19.62/12.82 inference(tautology,[status(thm)],[])).
% 19.62/12.82 tff(565,plain,
% 19.62/12.82 (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))),
% 19.62/12.82 inference(unit_resolution,[status(thm)],[564, 563, 534])).
% 19.62/12.88 tff(566,plain,
% 19.62/12.88 (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)))),
% 19.62/12.88 inference(symmetry,[status(thm)],[565])).
% 19.62/12.88 tff(567,plain,
% 19.62/12.88 (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)))),
% 19.62/12.88 inference(transitivity,[status(thm)],[522, 566, 515])).
% 19.62/12.88 tff(568,plain,
% 19.62/12.88 (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))))),
% 19.62/12.88 inference(monotonicity,[status(thm)],[567])).
% 19.62/12.88 tff(569,plain,
% 19.62/12.88 (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)))),
% 19.62/12.88 inference(transitivity,[status(thm)],[568, 494, 374, 285, 263])).
% 19.62/12.88 tff(570,plain,
% 19.62/12.88 (((~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)))))),
% 19.62/12.88 inference(tautology,[status(thm)],[])).
% 19.62/12.88 tff(571,plain,
% 19.62/12.88 (~(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))))),
% 19.62/12.88 inference(unit_resolution,[status(thm)],[570, 147])).
% 19.62/12.88 tff(572,plain,
% 19.62/12.88 ($false),
% 19.62/12.88 inference(unit_resolution,[status(thm)],[571, 569])).
% 19.62/12.88 % SZS output end Proof
%------------------------------------------------------------------------------