TSTP Solution File: TOP036+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP036+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 01:55:59 EDT 2022
% Result : Theorem 3.34s 2.44s
% Output : Proof 3.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP036+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 29 10:37:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 3.34/2.44 % SZS status Theorem
% 3.34/2.44 % SZS output start Proof
% 3.34/2.44 tff(v1_xboole_0_type, type, (
% 3.34/2.44 v1_xboole_0: $i > $o)).
% 3.34/2.44 tff(k4_tex_4_type, type, (
% 3.34/2.44 k4_tex_4: ( $i * $i ) > $i)).
% 3.34/2.44 tff(tptp_fun_C_2_type, type, (
% 3.34/2.44 tptp_fun_C_2: $i)).
% 3.34/2.44 tff(tptp_fun_A_0_type, type, (
% 3.34/2.44 tptp_fun_A_0: $i)).
% 3.34/2.44 tff(k1_xboole_0_type, type, (
% 3.34/2.44 k1_xboole_0: $i)).
% 3.34/2.44 tff(k2_tex_4_type, type, (
% 3.34/2.44 k2_tex_4: ( $i * $i ) > $i)).
% 3.34/2.44 tff(r1_tarski_type, type, (
% 3.34/2.44 r1_tarski: ( $i * $i ) > $o)).
% 3.34/2.44 tff(k1_relat_1_type, type, (
% 3.34/2.44 k1_relat_1: $i > $i)).
% 3.34/2.44 tff(k1_tsp_2_type, type, (
% 3.34/2.44 k1_tsp_2: ( $i * $i ) > $i)).
% 3.34/2.44 tff(tptp_fun_B_1_type, type, (
% 3.34/2.44 tptp_fun_B_1: $i)).
% 3.34/2.44 tff(u1_struct_0_type, type, (
% 3.34/2.44 u1_struct_0: $i > $i)).
% 3.34/2.44 tff(k2_pre_topc_type, type, (
% 3.34/2.44 k2_pre_topc: $i > $i)).
% 3.34/2.44 tff(l1_struct_0_type, type, (
% 3.34/2.44 l1_struct_0: $i > $o)).
% 3.34/2.44 tff(l1_pre_topc_type, type, (
% 3.34/2.44 l1_pre_topc: $i > $o)).
% 3.34/2.44 tff(k4_pre_topc_type, type, (
% 3.34/2.44 k4_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 3.34/2.44 tff(k3_tsp_2_type, type, (
% 3.34/2.44 k3_tsp_2: ( $i * $i ) > $i)).
% 3.34/2.44 tff(k1_struct_0_type, type, (
% 3.34/2.44 k1_struct_0: ( $i * $i ) > $i)).
% 3.34/2.44 tff(m1_subset_1_type, type, (
% 3.34/2.44 m1_subset_1: ( $i * $i ) > $o)).
% 3.34/2.44 tff(m2_tsp_1_type, type, (
% 3.34/2.44 m2_tsp_1: ( $i * $i ) > $o)).
% 3.34/2.44 tff(v2_tsp_2_type, type, (
% 3.34/2.44 v2_tsp_2: ( $i * $i ) > $o)).
% 3.34/2.44 tff(v3_struct_0_type, type, (
% 3.34/2.44 v3_struct_0: $i > $o)).
% 3.34/2.44 tff(v2_pre_topc_type, type, (
% 3.34/2.44 v2_pre_topc: $i > $o)).
% 3.34/2.44 tff(k2_relat_1_type, type, (
% 3.34/2.44 k2_relat_1: $i > $i)).
% 3.34/2.44 tff(m2_relset_1_type, type, (
% 3.34/2.44 m2_relset_1: ( $i * $i * $i ) > $o)).
% 3.34/2.44 tff(v1_funct_2_type, type, (
% 3.34/2.44 v1_funct_2: ( $i * $i * $i ) > $o)).
% 3.34/2.44 tff(v1_funct_1_type, type, (
% 3.34/2.44 v1_funct_1: $i > $o)).
% 3.34/2.44 tff(v5_pre_topc_type, type, (
% 3.34/2.44 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 3.34/2.44 tff(m1_pre_topc_type, type, (
% 3.34/2.44 m1_pre_topc: ( $i * $i ) > $o)).
% 3.34/2.44 tff(k1_zfmisc_1_type, type, (
% 3.34/2.44 k1_zfmisc_1: $i > $i)).
% 3.34/2.44 tff(k9_relat_1_type, type, (
% 3.34/2.44 k9_relat_1: ( $i * $i ) > $i)).
% 3.34/2.44 tff(k1_tarski_type, type, (
% 3.34/2.44 k1_tarski: $i > $i)).
% 3.34/2.44 tff(k1_funct_1_type, type, (
% 3.34/2.44 k1_funct_1: ( $i * $i ) > $i)).
% 3.34/2.44 tff(k8_funct_2_type, type, (
% 3.34/2.44 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 3.34/2.44 tff(k10_relat_1_type, type, (
% 3.34/2.44 k10_relat_1: ( $i * $i ) > $i)).
% 3.34/2.44 tff(m1_relset_1_type, type, (
% 3.34/2.44 m1_relset_1: ( $i * $i * $i ) > $o)).
% 3.34/2.44 tff(k5_pre_topc_type, type, (
% 3.34/2.44 k5_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 3.34/2.44 tff(v1_relat_1_type, type, (
% 3.34/2.44 v1_relat_1: $i > $o)).
% 3.34/2.44 tff(k2_zfmisc_1_type, type, (
% 3.34/2.44 k2_zfmisc_1: ( $i * $i ) > $i)).
% 3.34/2.44 tff(r2_hidden_type, type, (
% 3.34/2.44 r2_hidden: ( $i * $i ) > $o)).
% 3.34/2.44 tff(v1_membered_type, type, (
% 3.34/2.44 v1_membered: $i > $o)).
% 3.34/2.44 tff(v2_membered_type, type, (
% 3.34/2.44 v2_membered: $i > $o)).
% 3.34/2.44 tff(v3_membered_type, type, (
% 3.34/2.44 v3_membered: $i > $o)).
% 3.34/2.44 tff(v4_membered_type, type, (
% 3.34/2.44 v4_membered: $i > $o)).
% 3.34/2.44 tff(v5_membered_type, type, (
% 3.34/2.44 v5_membered: $i > $o)).
% 3.34/2.44 tff(1,plain,
% 3.34/2.44 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 3.34/2.44 inference(bind,[status(th)],[])).
% 3.34/2.44 tff(2,plain,
% 3.34/2.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(quant_intro,[status(thm)],[1])).
% 3.34/2.44 tff(3,plain,
% 3.34/2.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(4,plain,
% 3.34/2.44 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 3.34/2.44 inference(bind,[status(th)],[])).
% 3.34/2.44 tff(5,plain,
% 3.34/2.44 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(quant_intro,[status(thm)],[4])).
% 3.34/2.44 tff(6,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 3.34/2.44 tff(7,plain,
% 3.34/2.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 3.34/2.44 tff(8,plain,
% 3.34/2.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 3.34/2.44 tff(9,plain,(
% 3.34/2.44 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(skolemize,[status(sab)],[8])).
% 3.34/2.44 tff(10,plain,
% 3.34/2.44 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 3.34/2.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 3.34/2.44 tff(11,plain,
% 3.34/2.44 ((((~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) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))) <=> ((~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) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(12,plain,
% 3.34/2.44 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(13,plain,
% 3.34/2.44 ((~(~((~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))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(14,plain,
% 3.34/2.44 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))) <=> (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 3.34/2.44 inference(monotonicity,[status(thm)],[13])).
% 3.34/2.44 tff(15,plain,
% 3.34/2.44 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 3.34/2.44 inference(transitivity,[status(thm)],[14, 12])).
% 3.34/2.44 tff(16,plain,
% 3.34/2.44 ((~(~((~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))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(17,plain,
% 3.34/2.44 (((~(~((~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)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))) <=> (((~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) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))))),
% 3.34/2.44 inference(monotonicity,[status(thm)],[16, 15])).
% 3.34/2.44 tff(18,plain,
% 3.34/2.44 (((~(~((~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)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))) <=> ((~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) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 3.34/2.44 inference(transitivity,[status(thm)],[17, 11])).
% 3.34/2.44 tff(19,plain,
% 3.34/2.44 ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))) <=> (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C)))))))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(20,plain,
% 3.34/2.44 ((~![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] : (m1_subset_1(C, u1_struct_0(A)) => (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))) <=> (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C)))))))),
% 3.34/2.44 inference(rewrite,[status(thm)],[])).
% 3.34/2.44 tff(21,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] : (m1_subset_1(C, u1_struct_0(A)) => (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_tsp_2')).
% 3.34/2.44 tff(22,plain,
% 3.34/2.44 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 3.34/2.44 tff(23,plain,
% 3.34/2.44 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.44 inference(modus_ponens,[status(thm)],[22, 19])).
% 3.34/2.44 tff(24,plain,
% 3.34/2.44 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.44 inference(modus_ponens,[status(thm)],[23, 19])).
% 3.34/2.44 tff(25,plain,
% 3.34/2.44 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[24, 19])).
% 3.34/2.45 tff(26,plain,
% 3.34/2.45 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[25, 19])).
% 3.34/2.45 tff(27,plain,
% 3.34/2.45 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[26, 19])).
% 3.34/2.45 tff(28,plain,
% 3.34/2.45 (~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[27, 19])).
% 3.34/2.45 tff(29,plain,
% 3.34/2.45 ((~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) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[28, 18])).
% 3.34/2.45 tff(30,plain,
% 3.34/2.45 (l1_pre_topc(A!0)),
% 3.34/2.45 inference(and_elim,[status(thm)],[29])).
% 3.34/2.45 tff(31,plain,
% 3.34/2.45 (((~![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)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(32,plain,
% 3.34/2.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(33,plain,
% 3.34/2.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 3.34/2.45 tff(34,plain,
% 3.34/2.45 (l1_struct_0(A!0)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[33, 30, 10])).
% 3.34/2.45 tff(35,plain,
% 3.34/2.45 (^[A: $i] : refl(((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(36,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[35])).
% 3.34/2.45 tff(37,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(38,plain,
% 3.34/2.45 (^[A: $i] : rewrite((l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A))) <=> ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(39,plain,
% 3.34/2.45 (![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[38])).
% 3.34/2.45 tff(40,axiom,(![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_pre_topc')).
% 3.34/2.45 tff(41,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.34/2.45 tff(42,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 3.34/2.45 tff(43,plain,(
% 3.34/2.45 ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(skolemize,[status(sab)],[42])).
% 3.34/2.45 tff(44,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 3.34/2.45 tff(45,plain,
% 3.34/2.45 (((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | (~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(46,plain,
% 3.34/2.45 ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(47,plain,
% 3.34/2.45 ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | (~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.34/2.45 tff(48,plain,
% 3.34/2.45 (k2_pre_topc(A!0) = u1_struct_0(A!0)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 3.34/2.45 tff(49,plain,
% 3.34/2.45 (^[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)))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(50,plain,
% 3.34/2.45 (![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))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[49])).
% 3.34/2.45 tff(51,plain,
% 3.34/2.45 (^[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)))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(52,plain,
% 3.34/2.45 (![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))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[51])).
% 3.34/2.45 tff(53,plain,
% 3.34/2.45 (![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))))),
% 3.34/2.45 inference(transitivity,[status(thm)],[52, 50])).
% 3.34/2.45 tff(54,plain,
% 3.34/2.45 (![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))))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(55,plain,
% 3.34/2.45 (^[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))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(56,plain,
% 3.34/2.45 (![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))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[55])).
% 3.34/2.45 tff(57,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')).
% 3.34/2.45 tff(58,plain,
% 3.34/2.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.34/2.45 tff(59,plain,
% 3.34/2.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[58, 54])).
% 3.34/2.45 tff(60,plain,(
% 3.34/2.45 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 3.34/2.45 inference(skolemize,[status(sab)],[59])).
% 3.34/2.45 tff(61,plain,
% 3.34/2.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[60, 53])).
% 3.34/2.45 tff(62,plain,
% 3.34/2.45 (((~![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))))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(63,plain,
% 3.34/2.45 ((~![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))))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(64,plain,
% 3.34/2.45 ((~![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)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 3.34/2.45 tff(65,plain,
% 3.34/2.45 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[64, 30, 61])).
% 3.34/2.45 tff(66,plain,
% 3.34/2.45 (m2_tsp_1(B!1, A!0)),
% 3.34/2.45 inference(and_elim,[status(thm)],[29])).
% 3.34/2.45 tff(67,plain,
% 3.34/2.45 (((~![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)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(68,plain,
% 3.34/2.45 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(69,plain,
% 3.34/2.45 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.34/2.45 tff(70,plain,
% 3.34/2.45 (l1_pre_topc(B!1)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[69, 66, 65])).
% 3.34/2.45 tff(71,plain,
% 3.34/2.45 (((~![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)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(72,plain,
% 3.34/2.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(73,plain,
% 3.34/2.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 3.34/2.45 tff(74,plain,
% 3.34/2.45 (l1_struct_0(B!1)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[73, 10, 70])).
% 3.34/2.45 tff(75,plain,
% 3.34/2.45 (^[A: $i] : refl(((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(76,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[75])).
% 3.34/2.45 tff(77,plain,
% 3.34/2.45 (^[A: $i] : rewrite(((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(78,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[77])).
% 3.34/2.45 tff(79,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(transitivity,[status(thm)],[78, 76])).
% 3.34/2.45 tff(80,plain,
% 3.34/2.45 (^[A: $i] : rewrite(((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(81,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[80])).
% 3.34/2.45 tff(82,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(83,plain,
% 3.34/2.45 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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)))), ((((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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))), ((((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> (((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), rewrite((((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))), ((((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))), (![B: $i] : (((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), ((l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> (l1_struct_0(A) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))), rewrite((l1_struct_0(A) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), ((l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(84,plain,
% 3.34/2.45 (![A: $i] : (l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[83])).
% 3.34/2.45 tff(85,axiom,(![A: $i] : (l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_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))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t51_tops_2')).
% 3.34/2.45 tff(86,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 3.34/2.45 tff(87,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 3.34/2.45 tff(88,plain,(
% 3.34/2.45 ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_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)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 3.34/2.45 inference(skolemize,[status(sab)],[87])).
% 3.34/2.45 tff(89,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[88, 81])).
% 3.34/2.45 tff(90,plain,
% 3.34/2.45 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[89, 79])).
% 3.34/2.45 tff(91,plain,
% 3.34/2.45 (((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | (~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(92,plain,
% 3.34/2.45 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(93,plain,
% 3.34/2.45 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | (~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 3.34/2.45 tff(94,plain,
% 3.34/2.45 (![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[93, 90, 34])).
% 3.34/2.45 tff(95,plain,
% 3.34/2.45 (~v3_struct_0(B!1)),
% 3.34/2.45 inference(and_elim,[status(thm)],[29])).
% 3.34/2.45 tff(96,plain,
% 3.34/2.45 (((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | (v3_struct_0(B!1) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1)))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | v3_struct_0(B!1) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1)))))))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(97,plain,
% 3.34/2.45 ((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | (v3_struct_0(B!1) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1)))))))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(98,plain,
% 3.34/2.45 ((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | v3_struct_0(B!1) | (~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 3.34/2.45 tff(99,plain,
% 3.34/2.45 ((~l1_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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[98, 95, 94])).
% 3.34/2.45 tff(100,plain,
% 3.34/2.45 (![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[99, 74])).
% 3.34/2.45 tff(101,plain,
% 3.34/2.45 (^[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))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(102,plain,
% 3.34/2.45 (![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)))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[101])).
% 3.34/2.45 tff(103,plain,
% 3.34/2.45 (^[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))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(104,plain,
% 3.34/2.45 (![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)))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[103])).
% 3.34/2.45 tff(105,plain,
% 3.34/2.45 (![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)))),
% 3.34/2.45 inference(transitivity,[status(thm)],[104, 102])).
% 3.34/2.45 tff(106,plain,
% 3.34/2.45 (![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)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(107,plain,
% 3.34/2.45 (^[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))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(108,plain,
% 3.34/2.45 (![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)))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[107])).
% 3.34/2.45 tff(109,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')).
% 3.34/2.45 tff(110,plain,
% 3.34/2.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 3.34/2.45 tff(111,plain,
% 3.34/2.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[110, 106])).
% 3.34/2.45 tff(112,plain,(
% 3.34/2.45 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 3.34/2.45 inference(skolemize,[status(sab)],[111])).
% 3.34/2.45 tff(113,plain,
% 3.34/2.45 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[112, 105])).
% 3.34/2.45 tff(114,plain,
% 3.34/2.45 (((~![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)))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(115,plain,
% 3.34/2.45 ((~![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)))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(116,plain,
% 3.34/2.45 ((~![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))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 3.34/2.45 tff(117,plain,
% 3.34/2.45 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[116, 30, 113])).
% 3.34/2.45 tff(118,plain,
% 3.34/2.45 ((~![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))),
% 3.34/2.45 inference(quant_inst,[status(thm)],[])).
% 3.34/2.45 tff(119,plain,
% 3.34/2.45 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[118, 117])).
% 3.34/2.45 tff(120,plain,
% 3.34/2.45 ((~(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)),
% 3.34/2.45 inference(tautology,[status(thm)],[])).
% 3.34/2.45 tff(121,plain,
% 3.34/2.45 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[120, 66])).
% 3.34/2.45 tff(122,plain,
% 3.34/2.45 (m1_pre_topc(B!1, A!0)),
% 3.34/2.45 inference(unit_resolution,[status(thm)],[121, 119])).
% 3.34/2.45 tff(123,plain,
% 3.34/2.45 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(124,plain,
% 3.34/2.45 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[123])).
% 3.34/2.45 tff(125,plain,
% 3.34/2.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(126,plain,
% 3.34/2.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[125])).
% 3.34/2.45 tff(127,plain,
% 3.34/2.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.34/2.45 inference(rewrite,[status(thm)],[])).
% 3.34/2.45 tff(128,plain,
% 3.34/2.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(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)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), trans(monotonicity(rewrite(((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B))), ((((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.34/2.45 inference(bind,[status(th)],[])).
% 3.34/2.45 tff(129,plain,
% 3.34/2.45 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.34/2.45 inference(quant_intro,[status(thm)],[128])).
% 3.34/2.45 tff(130,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tsp_2')).
% 3.34/2.45 tff(131,plain,
% 3.34/2.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 3.34/2.45 tff(132,plain,
% 3.34/2.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[131, 127])).
% 3.34/2.45 tff(133,plain,(
% 3.34/2.45 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.34/2.45 inference(skolemize,[status(sab)],[132])).
% 3.34/2.45 tff(134,plain,
% 3.34/2.45 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.34/2.45 inference(modus_ponens,[status(thm)],[133, 126])).
% 3.34/2.45 tff(135,plain,
% 3.34/2.45 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[134, 124])).
% 3.34/2.46 tff(136,plain,
% 3.34/2.46 (v2_tsp_2(B!1, A!0)),
% 3.34/2.46 inference(and_elim,[status(thm)],[29])).
% 3.34/2.46 tff(137,plain,
% 3.34/2.46 (v2_pre_topc(A!0)),
% 3.34/2.46 inference(and_elim,[status(thm)],[29])).
% 3.34/2.46 tff(138,plain,
% 3.34/2.46 (~v3_struct_0(A!0)),
% 3.34/2.46 inference(and_elim,[status(thm)],[29])).
% 3.34/2.46 tff(139,plain,
% 3.34/2.46 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(140,plain,
% 3.34/2.46 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(141,plain,
% 3.34/2.46 ((~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(142,plain,
% 3.34/2.46 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.34/2.46 inference(monotonicity,[status(thm)],[141])).
% 3.34/2.46 tff(143,plain,
% 3.34/2.46 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.34/2.46 inference(transitivity,[status(thm)],[142, 140])).
% 3.34/2.46 tff(144,plain,
% 3.34/2.46 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 3.34/2.46 inference(monotonicity,[status(thm)],[143])).
% 3.34/2.46 tff(145,plain,
% 3.34/2.46 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.34/2.46 inference(transitivity,[status(thm)],[144, 139])).
% 3.34/2.46 tff(146,plain,
% 3.34/2.46 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.34/2.46 inference(quant_inst,[status(thm)],[])).
% 3.34/2.46 tff(147,plain,
% 3.34/2.46 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 3.34/2.46 tff(148,plain,
% 3.34/2.46 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[147, 138, 137, 30, 95, 136, 135])).
% 3.34/2.46 tff(149,plain,
% 3.34/2.46 (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[148, 122])).
% 3.34/2.46 tff(150,plain,
% 3.34/2.46 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.34/2.46 inference(tautology,[status(thm)],[])).
% 3.34/2.46 tff(151,plain,
% 3.34/2.46 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[150, 149])).
% 3.34/2.46 tff(152,plain,
% 3.34/2.46 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.34/2.46 inference(tautology,[status(thm)],[])).
% 3.34/2.46 tff(153,plain,
% 3.34/2.46 (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[152, 149])).
% 3.34/2.46 tff(154,plain,
% 3.34/2.46 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k1_tsp_2(A!0, B!1))),
% 3.34/2.46 inference(tautology,[status(thm)],[])).
% 3.34/2.46 tff(155,plain,
% 3.34/2.46 (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[154, 149])).
% 3.34/2.46 tff(156,plain,
% 3.34/2.46 (((~![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(157,plain,
% 3.34/2.46 ((~![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))))),
% 3.34/2.46 inference(quant_inst,[status(thm)],[])).
% 3.34/2.46 tff(158,plain,
% 3.34/2.46 ((~![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))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1)))))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[157, 156])).
% 3.34/2.46 tff(159,plain,
% 3.34/2.46 (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[158, 155, 153, 151, 100])).
% 3.34/2.46 tff(160,plain,
% 3.34/2.46 (((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1)))) | (k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))),
% 3.34/2.46 inference(tautology,[status(thm)],[])).
% 3.34/2.46 tff(161,plain,
% 3.34/2.46 (k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0)),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[160, 159])).
% 3.34/2.46 tff(162,plain,
% 3.34/2.46 (k1_relat_1(k1_tsp_2(A!0, B!1)) = u1_struct_0(A!0)),
% 3.34/2.46 inference(transitivity,[status(thm)],[161, 48])).
% 3.34/2.46 tff(163,plain,
% 3.34/2.46 (r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 3.34/2.46 inference(monotonicity,[status(thm)],[162])).
% 3.34/2.46 tff(164,plain,
% 3.34/2.46 (r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)) <=> r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 3.34/2.46 inference(symmetry,[status(thm)],[163])).
% 3.34/2.46 tff(165,plain,
% 3.34/2.46 (^[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)))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(166,plain,
% 3.34/2.46 (![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))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[165])).
% 3.34/2.46 tff(167,plain,
% 3.34/2.46 (![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))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(168,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')).
% 3.34/2.46 tff(169,plain,
% 3.34/2.46 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.34/2.46 tff(170,plain,(
% 3.34/2.46 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 3.34/2.46 inference(skolemize,[status(sab)],[169])).
% 3.34/2.46 tff(171,plain,
% 3.34/2.46 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[170, 166])).
% 3.34/2.46 tff(172,plain,
% 3.34/2.46 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)))),
% 3.34/2.46 inference(quant_inst,[status(thm)],[])).
% 3.34/2.46 tff(173,plain,
% 3.34/2.46 (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[172, 171])).
% 3.34/2.46 tff(174,plain,
% 3.34/2.46 (^[A: $i, B: $i] : refl((m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A))) <=> (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(175,plain,
% 3.34/2.46 (![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[174])).
% 3.34/2.46 tff(176,plain,
% 3.34/2.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))), (((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(177,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[176])).
% 3.34/2.46 tff(178,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(179,plain,
% 3.34/2.46 (^[A: $i, B: $i] : rewrite(((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(180,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[179])).
% 3.34/2.46 tff(181,axiom,(![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_tex_4')).
% 3.34/2.46 tff(182,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[181, 180])).
% 3.34/2.46 tff(183,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[182, 178])).
% 3.34/2.46 tff(184,plain,(
% 3.34/2.46 ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 3.34/2.46 inference(skolemize,[status(sab)],[183])).
% 3.34/2.46 tff(185,plain,
% 3.34/2.46 (![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[184, 177])).
% 3.34/2.46 tff(186,plain,
% 3.34/2.46 (![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[185, 175])).
% 3.34/2.46 tff(187,plain,
% 3.34/2.46 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 3.34/2.46 inference(and_elim,[status(thm)],[29])).
% 3.34/2.46 tff(188,plain,
% 3.34/2.46 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 3.34/2.46 inference(or_elim,[status(thm)],[187])).
% 3.34/2.46 tff(189,plain,
% 3.34/2.46 (((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(190,plain,
% 3.34/2.46 ((m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(191,plain,
% 3.34/2.46 (((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 3.34/2.46 inference(monotonicity,[status(thm)],[190])).
% 3.34/2.46 tff(192,plain,
% 3.34/2.46 (((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 3.34/2.46 inference(transitivity,[status(thm)],[191, 189])).
% 3.34/2.46 tff(193,plain,
% 3.34/2.46 ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)))),
% 3.34/2.46 inference(quant_inst,[status(thm)],[])).
% 3.34/2.46 tff(194,plain,
% 3.34/2.46 ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[193, 192])).
% 3.34/2.46 tff(195,plain,
% 3.34/2.46 (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[194, 30, 188, 186])).
% 3.34/2.46 tff(196,plain,
% 3.34/2.46 ((~(m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)))) | (~m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 3.34/2.46 inference(tautology,[status(thm)],[])).
% 3.34/2.46 tff(197,plain,
% 3.34/2.46 ((~(m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)))) | r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[196, 195])).
% 3.34/2.46 tff(198,plain,
% 3.34/2.46 (r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[197, 173])).
% 3.34/2.46 tff(199,plain,
% 3.34/2.46 (r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[198, 164])).
% 3.34/2.46 tff(200,plain,
% 3.34/2.46 (^[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))) | (~v2_pre_topc(A)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(201,plain,
% 3.34/2.46 (![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))) | (~v2_pre_topc(A)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[200])).
% 3.34/2.46 tff(202,plain,
% 3.34/2.46 (^[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))) | (~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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_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) | (~m1_subset_1(B, u1_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)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_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))) | (~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)))) | (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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(203,plain,
% 3.34/2.46 (![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[202])).
% 3.34/2.46 tff(204,plain,
% 3.34/2.46 (![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)))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(205,plain,
% 3.34/2.46 (^[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)))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(206,plain,
% 3.34/2.46 (![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)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[205])).
% 3.34/2.46 tff(207,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')).
% 3.34/2.46 tff(208,plain,
% 3.34/2.46 (![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)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[207, 206])).
% 3.34/2.46 tff(209,plain,
% 3.34/2.46 (![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)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[208, 204])).
% 3.34/2.46 tff(210,plain,(
% 3.34/2.46 ![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)))),
% 3.34/2.46 inference(skolemize,[status(sab)],[209])).
% 3.34/2.46 tff(211,plain,
% 3.34/2.46 (![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[210, 203])).
% 3.34/2.46 tff(212,plain,
% 3.34/2.46 (![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[211, 201])).
% 3.34/2.46 tff(213,plain,
% 3.34/2.46 (((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))) <=> ((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(214,plain,
% 3.34/2.46 ((v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(215,plain,
% 3.34/2.46 (((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2))))),
% 3.34/2.46 inference(monotonicity,[status(thm)],[214])).
% 3.34/2.46 tff(216,plain,
% 3.34/2.46 (((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))),
% 3.34/2.46 inference(transitivity,[status(thm)],[215, 213])).
% 3.34/2.46 tff(217,plain,
% 3.34/2.46 ((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))),
% 3.34/2.46 inference(quant_inst,[status(thm)],[])).
% 3.34/2.46 tff(218,plain,
% 3.34/2.46 ((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2))),
% 3.34/2.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 3.34/2.46 tff(219,plain,
% 3.34/2.46 (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)),
% 3.34/2.46 inference(unit_resolution,[status(thm)],[218, 138, 137, 30, 188, 212])).
% 3.34/2.46 tff(220,plain,
% 3.34/2.46 (k2_tex_4(A!0, C!2) = k4_tex_4(A!0, C!2)),
% 3.34/2.46 inference(symmetry,[status(thm)],[219])).
% 3.34/2.46 tff(221,plain,
% 3.34/2.46 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(222,plain,
% 3.34/2.46 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[221])).
% 3.34/2.46 tff(223,plain,
% 3.34/2.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))))),
% 3.34/2.46 inference(bind,[status(th)],[])).
% 3.34/2.46 tff(224,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.46 inference(quant_intro,[status(thm)],[223])).
% 3.34/2.46 tff(225,plain,
% 3.34/2.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 3.34/2.46 inference(rewrite,[status(thm)],[])).
% 3.34/2.46 tff(226,plain,
% 3.34/2.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(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)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))))),
% 3.34/2.47 inference(bind,[status(th)],[])).
% 3.34/2.47 tff(227,plain,
% 3.34/2.47 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 3.34/2.47 inference(quant_intro,[status(thm)],[226])).
% 3.34/2.47 tff(228,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_tsp_2')).
% 3.34/2.47 tff(229,plain,
% 3.34/2.47 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 3.34/2.47 inference(modus_ponens,[status(thm)],[228, 227])).
% 3.34/2.47 tff(230,plain,
% 3.34/2.47 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 3.34/2.47 inference(modus_ponens,[status(thm)],[229, 225])).
% 3.34/2.47 tff(231,plain,(
% 3.34/2.47 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 3.34/2.47 inference(skolemize,[status(sab)],[230])).
% 3.34/2.47 tff(232,plain,
% 3.34/2.47 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.47 inference(modus_ponens,[status(thm)],[231, 224])).
% 3.34/2.47 tff(233,plain,
% 3.34/2.47 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 3.34/2.47 inference(modus_ponens,[status(thm)],[232, 222])).
% 3.34/2.47 tff(234,plain,
% 3.34/2.47 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 3.34/2.47 inference(rewrite,[status(thm)],[])).
% 3.34/2.47 tff(235,plain,
% 3.34/2.47 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 3.34/2.47 inference(rewrite,[status(thm)],[])).
% 3.34/2.47 tff(236,plain,
% 3.34/2.47 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))))),
% 3.34/2.47 inference(monotonicity,[status(thm)],[235])).
% 3.34/2.47 tff(237,plain,
% 3.34/2.47 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 3.34/2.47 inference(transitivity,[status(thm)],[236, 234])).
% 3.34/2.47 tff(238,plain,
% 3.34/2.47 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))),
% 3.34/2.47 inference(quant_inst,[status(thm)],[])).
% 3.34/2.47 tff(239,plain,
% 3.34/2.47 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 3.34/2.47 inference(modus_ponens,[status(thm)],[238, 237])).
% 3.34/2.47 tff(240,plain,
% 3.34/2.47 ((k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 3.34/2.47 inference(unit_resolution,[status(thm)],[239, 138, 137, 30, 95, 136, 233])).
% 3.34/2.47 tff(241,plain,
% 3.34/2.47 (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)),
% 3.34/2.47 inference(unit_resolution,[status(thm)],[240, 122])).
% 3.34/2.47 tff(242,plain,
% 3.34/2.47 (k1_tsp_2(A!0, B!1) = k3_tsp_2(A!0, B!1)),
% 3.34/2.47 inference(symmetry,[status(thm)],[241])).
% 3.34/2.47 tff(243,plain,
% 3.34/2.47 (k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))),
% 3.34/2.47 inference(monotonicity,[status(thm)],[242, 220])).
% 3.34/2.47 tff(244,plain,
% 3.34/2.47 (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2))),
% 3.34/2.47 inference(symmetry,[status(thm)],[243])).
% 3.34/2.47 tff(245,plain,
% 3.34/2.47 ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) <=> (k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)),
% 3.34/2.47 inference(monotonicity,[status(thm)],[244])).
% 3.34/2.47 tff(246,plain,
% 3.34/2.47 (^[A: $i, B: $i] : refl((r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))) <=> (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))))),
% 3.34/2.47 inference(bind,[status(th)],[])).
% 3.34/2.47 tff(247,plain,
% 3.34/2.47 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))) <=> ![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 3.34/2.47 inference(quant_intro,[status(thm)],[246])).
% 3.34/2.47 tff(248,plain,
% 3.34/2.47 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))) <=> ![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(249,axiom,(![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t39_zfmisc_1')).
% 3.48/2.47 tff(250,plain,
% 3.48/2.47 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[249, 248])).
% 3.48/2.47 tff(251,plain,(
% 3.48/2.47 ![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 3.48/2.47 inference(skolemize,[status(sab)],[250])).
% 3.48/2.47 tff(252,plain,
% 3.48/2.47 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[251, 247])).
% 3.48/2.47 tff(253,plain,
% 3.48/2.47 ((~![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))) | (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))))),
% 3.48/2.47 inference(quant_inst,[status(thm)],[])).
% 3.48/2.47 tff(254,plain,
% 3.48/2.47 (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[253, 252])).
% 3.48/2.47 tff(255,plain,
% 3.48/2.47 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2)),
% 3.48/2.47 inference(monotonicity,[status(thm)],[241])).
% 3.48/2.47 tff(256,plain,
% 3.48/2.47 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) <=> m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 3.48/2.47 inference(monotonicity,[status(thm)],[255])).
% 3.48/2.47 tff(257,plain,
% 3.48/2.47 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) <=> m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 3.48/2.47 inference(symmetry,[status(thm)],[256])).
% 3.48/2.47 tff(258,plain,
% 3.48/2.47 (^[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)))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(259,plain,
% 3.48/2.47 (![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))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[258])).
% 3.48/2.47 tff(260,plain,
% 3.48/2.47 (![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))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(261,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')).
% 3.48/2.47 tff(262,plain,
% 3.48/2.47 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[261, 260])).
% 3.48/2.47 tff(263,plain,(
% 3.48/2.47 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.48/2.47 inference(skolemize,[status(sab)],[262])).
% 3.48/2.47 tff(264,plain,
% 3.48/2.47 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[263, 259])).
% 3.48/2.47 tff(265,plain,
% 3.48/2.47 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 3.48/2.47 inference(quant_inst,[status(thm)],[])).
% 3.48/2.47 tff(266,plain,
% 3.48/2.47 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[265, 264])).
% 3.48/2.47 tff(267,plain,
% 3.48/2.47 ((~(m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.48/2.47 inference(tautology,[status(thm)],[])).
% 3.48/2.47 tff(268,plain,
% 3.48/2.47 ((~(m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[267, 151])).
% 3.48/2.47 tff(269,plain,
% 3.48/2.47 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[268, 266])).
% 3.48/2.47 tff(270,plain,
% 3.48/2.47 (^[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))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(271,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[270])).
% 3.48/2.47 tff(272,plain,
% 3.48/2.47 (^[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)))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(273,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[272])).
% 3.48/2.47 tff(274,plain,
% 3.48/2.47 (![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))))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(275,plain,
% 3.48/2.47 (^[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)))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(276,plain,
% 3.48/2.47 (![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))))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[275])).
% 3.48/2.47 tff(277,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')).
% 3.48/2.47 tff(278,plain,
% 3.48/2.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[277, 276])).
% 3.48/2.47 tff(279,plain,
% 3.48/2.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[278, 274])).
% 3.48/2.47 tff(280,plain,(
% 3.48/2.47 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.48/2.47 inference(skolemize,[status(sab)],[279])).
% 3.48/2.47 tff(281,plain,
% 3.48/2.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[280, 273])).
% 3.48/2.47 tff(282,plain,
% 3.48/2.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[281, 271])).
% 3.48/2.47 tff(283,plain,
% 3.48/2.47 (((~![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))))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(284,plain,
% 3.48/2.47 ((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))))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(285,plain,
% 3.48/2.47 (((~![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)))))),
% 3.48/2.47 inference(monotonicity,[status(thm)],[284])).
% 3.48/2.47 tff(286,plain,
% 3.48/2.47 (((~![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))))),
% 3.48/2.47 inference(transitivity,[status(thm)],[285, 283])).
% 3.48/2.47 tff(287,plain,
% 3.48/2.47 ((~![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)))),
% 3.48/2.47 inference(quant_inst,[status(thm)],[])).
% 3.48/2.47 tff(288,plain,
% 3.48/2.47 ((~![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)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[287, 286])).
% 3.48/2.47 tff(289,plain,
% 3.48/2.47 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[288, 138, 282])).
% 3.48/2.47 tff(290,plain,
% 3.48/2.47 (~v1_xboole_0(u1_struct_0(A!0))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[289, 34])).
% 3.48/2.47 tff(291,plain,
% 3.48/2.47 (^[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))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(292,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[291])).
% 3.48/2.47 tff(293,plain,
% 3.48/2.47 (^[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)))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(294,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[293])).
% 3.48/2.47 tff(295,plain,
% 3.48/2.47 (![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))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(296,plain,
% 3.48/2.47 (^[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))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(297,plain,
% 3.48/2.47 (![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))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[296])).
% 3.48/2.47 tff(298,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')).
% 3.48/2.47 tff(299,plain,
% 3.48/2.47 (![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))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[298, 297])).
% 3.48/2.47 tff(300,plain,
% 3.48/2.47 (![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))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[299, 295])).
% 3.48/2.47 tff(301,plain,(
% 3.48/2.47 ![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))),
% 3.48/2.47 inference(skolemize,[status(sab)],[300])).
% 3.48/2.47 tff(302,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[301, 294])).
% 3.48/2.47 tff(303,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[302, 292])).
% 3.48/2.47 tff(304,plain,
% 3.48/2.47 (((~![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(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), 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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(305,plain,
% 3.48/2.47 ((m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(306,plain,
% 3.48/2.47 (((~![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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))),
% 3.48/2.47 inference(monotonicity,[status(thm)],[305])).
% 3.48/2.47 tff(307,plain,
% 3.48/2.47 (((~![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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)))),
% 3.48/2.47 inference(transitivity,[status(thm)],[306, 304])).
% 3.48/2.47 tff(308,plain,
% 3.48/2.47 ((~![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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.48/2.47 inference(quant_inst,[status(thm)],[])).
% 3.48/2.47 tff(309,plain,
% 3.48/2.47 ((~![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(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[308, 307])).
% 3.48/2.47 tff(310,plain,
% 3.48/2.47 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 3.48/2.47 inference(unit_resolution,[status(thm)],[309, 188, 303, 290, 155, 153, 269])).
% 3.48/2.47 tff(311,plain,
% 3.48/2.47 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[310, 257])).
% 3.48/2.47 tff(312,plain,
% 3.48/2.47 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(313,plain,
% 3.48/2.47 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[312])).
% 3.48/2.47 tff(314,plain,
% 3.48/2.47 (^[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)) | (~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) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(315,plain,
% 3.48/2.47 (![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)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[314])).
% 3.48/2.47 tff(316,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(317,plain,
% 3.48/2.47 (^[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)))))),
% 3.48/2.47 inference(bind,[status(th)],[])).
% 3.48/2.47 tff(318,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(quant_intro,[status(thm)],[317])).
% 3.48/2.47 tff(319,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')).
% 3.48/2.47 tff(320,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[319, 318])).
% 3.48/2.47 tff(321,plain,
% 3.48/2.47 (![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)))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[320, 316])).
% 3.48/2.47 tff(322,plain,(
% 3.48/2.47 ![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)))),
% 3.48/2.47 inference(skolemize,[status(sab)],[321])).
% 3.48/2.47 tff(323,plain,
% 3.48/2.47 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[322, 315])).
% 3.48/2.47 tff(324,plain,
% 3.48/2.47 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.48/2.47 inference(modus_ponens,[status(thm)],[323, 313])).
% 3.48/2.47 tff(325,plain,
% 3.48/2.47 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(326,plain,
% 3.48/2.47 ((v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.47 inference(rewrite,[status(thm)],[])).
% 3.48/2.47 tff(327,plain,
% 3.48/2.47 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 3.48/2.48 inference(monotonicity,[status(thm)],[326])).
% 3.48/2.48 tff(328,plain,
% 3.48/2.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.48 inference(transitivity,[status(thm)],[327, 325])).
% 3.48/2.48 tff(329,plain,
% 3.48/2.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))),
% 3.48/2.48 inference(quant_inst,[status(thm)],[])).
% 3.48/2.48 tff(330,plain,
% 3.48/2.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[329, 328])).
% 3.48/2.48 tff(331,plain,
% 3.48/2.48 ((~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.48 inference(unit_resolution,[status(thm)],[330, 95, 324, 74])).
% 3.48/2.48 tff(332,plain,
% 3.48/2.48 (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 3.48/2.48 inference(unit_resolution,[status(thm)],[331, 311])).
% 3.48/2.48 tff(333,plain,
% 3.48/2.48 (k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 3.48/2.48 inference(symmetry,[status(thm)],[332])).
% 3.48/2.48 tff(334,plain,
% 3.48/2.48 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)),
% 3.48/2.48 inference(symmetry,[status(thm)],[255])).
% 3.48/2.48 tff(335,plain,
% 3.48/2.48 (^[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))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(336,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[335])).
% 3.48/2.48 tff(337,plain,
% 3.48/2.48 (^[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)))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(338,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[337])).
% 3.48/2.48 tff(339,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(rewrite,[status(thm)],[])).
% 3.48/2.48 tff(340,plain,
% 3.48/2.48 (^[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)))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(341,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[340])).
% 3.48/2.48 tff(342,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')).
% 3.48/2.48 tff(343,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[342, 341])).
% 3.48/2.48 tff(344,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[343, 339])).
% 3.48/2.48 tff(345,plain,(
% 3.48/2.48 ![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)))),
% 3.48/2.48 inference(skolemize,[status(sab)],[344])).
% 3.48/2.48 tff(346,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[345, 338])).
% 3.48/2.48 tff(347,plain,
% 3.48/2.48 (![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)))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[346, 336])).
% 3.48/2.48 tff(348,plain,
% 3.48/2.48 (((~![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)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))) <=> ((~![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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.48 inference(rewrite,[status(thm)],[])).
% 3.48/2.48 tff(349,plain,
% 3.48/2.48 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.48 inference(rewrite,[status(thm)],[])).
% 3.48/2.48 tff(350,plain,
% 3.48/2.48 (((~![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), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.48 inference(monotonicity,[status(thm)],[349])).
% 3.48/2.48 tff(351,plain,
% 3.48/2.48 (((~![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), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.48 inference(transitivity,[status(thm)],[350, 348])).
% 3.48/2.48 tff(352,plain,
% 3.48/2.48 ((~![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), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.48/2.48 inference(quant_inst,[status(thm)],[])).
% 3.48/2.48 tff(353,plain,
% 3.48/2.48 ((~![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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[352, 351])).
% 3.48/2.48 tff(354,plain,
% 3.48/2.48 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)),
% 3.48/2.48 inference(unit_resolution,[status(thm)],[353, 188, 347, 290, 155, 153, 269])).
% 3.48/2.48 tff(355,plain,
% 3.48/2.48 (k1_funct_1(k1_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2)),
% 3.48/2.48 inference(symmetry,[status(thm)],[354])).
% 3.48/2.48 tff(356,plain,
% 3.48/2.48 (k1_funct_1(k1_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)),
% 3.48/2.48 inference(transitivity,[status(thm)],[355, 334])).
% 3.48/2.48 tff(357,plain,
% 3.48/2.48 (k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 3.48/2.48 inference(monotonicity,[status(thm)],[356])).
% 3.48/2.48 tff(358,plain,
% 3.48/2.48 (k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 3.48/2.48 inference(transitivity,[status(thm)],[357, 333])).
% 3.48/2.48 tff(359,plain,
% 3.48/2.48 (^[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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(360,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[359])).
% 3.48/2.48 tff(361,plain,
% 3.48/2.48 (^[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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(362,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[361])).
% 3.48/2.48 tff(363,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(transitivity,[status(thm)],[362, 360])).
% 3.48/2.48 tff(364,plain,
% 3.48/2.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((~((~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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ((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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), 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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((~((~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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(365,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[364])).
% 3.48/2.48 tff(366,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(rewrite,[status(thm)],[])).
% 3.48/2.48 tff(367,plain,
% 3.48/2.48 (^[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] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((((~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] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (((~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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), 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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ((~((~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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((((~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] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ((~((~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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))))),
% 3.48/2.48 inference(bind,[status(th)],[])).
% 3.48/2.48 tff(368,plain,
% 3.48/2.48 (![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] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(quant_intro,[status(thm)],[367])).
% 3.48/2.48 tff(369,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] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_tsp_2')).
% 3.48/2.48 tff(370,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[369, 368])).
% 3.48/2.48 tff(371,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[370, 366])).
% 3.48/2.48 tff(372,plain,(
% 3.48/2.48 ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(skolemize,[status(sab)],[371])).
% 3.48/2.48 tff(373,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[372, 365])).
% 3.48/2.48 tff(374,plain,
% 3.48/2.48 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[373, 363])).
% 3.48/2.48 tff(375,plain,
% 3.48/2.48 (((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C)))))) <=> ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | 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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C)))))),
% 3.48/2.48 inference(rewrite,[status(thm)],[])).
% 3.48/2.48 tff(376,plain,
% 3.48/2.48 ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C)))))),
% 3.48/2.48 inference(quant_inst,[status(thm)],[])).
% 3.48/2.48 tff(377,plain,
% 3.48/2.48 ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | 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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))),
% 3.48/2.48 inference(modus_ponens,[status(thm)],[376, 375])).
% 3.48/2.48 tff(378,plain,
% 3.48/2.48 (![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))),
% 3.48/2.48 inference(unit_resolution,[status(thm)],[377, 138, 137, 30, 374])).
% 3.48/2.48 tff(379,plain,
% 3.48/2.48 (((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))),
% 3.48/2.48 inference(rewrite,[status(thm)],[])).
% 3.48/2.48 tff(380,plain,
% 3.48/2.48 ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))),
% 3.48/2.49 inference(quant_inst,[status(thm)],[])).
% 3.48/2.49 tff(381,plain,
% 3.48/2.49 ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[380, 379])).
% 3.48/2.49 tff(382,plain,
% 3.48/2.49 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))),
% 3.48/2.49 inference(unit_resolution,[status(thm)],[381, 95, 136, 66, 378])).
% 3.48/2.49 tff(383,plain,
% 3.48/2.49 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(384,plain,
% 3.48/2.49 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)))),
% 3.48/2.49 inference(quant_inst,[status(thm)],[])).
% 3.48/2.49 tff(385,plain,
% 3.48/2.49 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[384, 383])).
% 3.48/2.49 tff(386,plain,
% 3.48/2.49 (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)),
% 3.48/2.49 inference(unit_resolution,[status(thm)],[385, 188, 382])).
% 3.48/2.49 tff(387,plain,
% 3.48/2.49 (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.49 inference(monotonicity,[status(thm)],[242])).
% 3.48/2.49 tff(388,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(389,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[388])).
% 3.48/2.49 tff(390,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> (((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))))), rewrite((((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(391,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[390])).
% 3.48/2.49 tff(392,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(393,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(394,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[393])).
% 3.48/2.49 tff(395,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_pre_topc')).
% 3.48/2.49 tff(396,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[395, 394])).
% 3.48/2.49 tff(397,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[396, 392])).
% 3.48/2.49 tff(398,plain,(
% 3.48/2.49 ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 3.48/2.49 inference(skolemize,[status(sab)],[397])).
% 3.48/2.49 tff(399,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[398, 391])).
% 3.48/2.49 tff(400,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[399, 389])).
% 3.48/2.49 tff(401,plain,
% 3.48/2.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(402,plain,
% 3.48/2.49 (((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(403,plain,
% 3.48/2.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))))),
% 3.48/2.49 inference(monotonicity,[status(thm)],[402])).
% 3.48/2.49 tff(404,plain,
% 3.48/2.49 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 3.48/2.49 inference(transitivity,[status(thm)],[403, 401])).
% 3.48/2.49 tff(405,plain,
% 3.48/2.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.48/2.49 inference(quant_inst,[status(thm)],[])).
% 3.48/2.49 tff(406,plain,
% 3.48/2.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[405, 404])).
% 3.48/2.49 tff(407,plain,
% 3.48/2.49 (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.49 inference(unit_resolution,[status(thm)],[406, 400, 34, 74, 155, 153, 269])).
% 3.48/2.49 tff(408,plain,
% 3.48/2.49 (k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.49 inference(symmetry,[status(thm)],[407])).
% 3.48/2.49 tff(409,plain,
% 3.48/2.49 (k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)),
% 3.48/2.49 inference(transitivity,[status(thm)],[408, 387, 386])).
% 3.48/2.49 tff(410,plain,
% 3.48/2.49 (k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))),
% 3.48/2.49 inference(monotonicity,[status(thm)],[242, 409])).
% 3.48/2.49 tff(411,plain,
% 3.48/2.49 (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 3.48/2.49 inference(symmetry,[status(thm)],[410])).
% 3.48/2.49 tff(412,plain,
% 3.48/2.49 (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.49 inference(monotonicity,[status(thm)],[411, 358])).
% 3.48/2.49 tff(413,plain,
% 3.48/2.49 (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) <=> r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.48/2.49 inference(symmetry,[status(thm)],[412])).
% 3.48/2.49 tff(414,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(415,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[414])).
% 3.48/2.49 tff(416,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(417,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(418,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[417])).
% 3.48/2.49 tff(419,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 3.48/2.49 tff(420,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[419, 418])).
% 3.48/2.49 tff(421,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[420, 416])).
% 3.48/2.49 tff(422,plain,(
% 3.48/2.49 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(skolemize,[status(sab)],[421])).
% 3.48/2.49 tff(423,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[422, 415])).
% 3.48/2.49 tff(424,plain,
% 3.48/2.49 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(425,plain,
% 3.48/2.49 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.48/2.49 inference(quant_inst,[status(thm)],[])).
% 3.48/2.49 tff(426,plain,
% 3.48/2.49 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[425, 424])).
% 3.48/2.49 tff(427,plain,
% 3.48/2.49 (m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.48/2.49 inference(unit_resolution,[status(thm)],[426, 423, 151])).
% 3.48/2.49 tff(428,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(429,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[428])).
% 3.48/2.49 tff(430,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(431,plain,
% 3.48/2.49 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(432,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[431])).
% 3.48/2.49 tff(433,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 3.48/2.49 tff(434,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[433, 432])).
% 3.48/2.49 tff(435,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[434, 430])).
% 3.48/2.49 tff(436,plain,(
% 3.48/2.49 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(skolemize,[status(sab)],[435])).
% 3.48/2.49 tff(437,plain,
% 3.48/2.49 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[436, 429])).
% 3.48/2.49 tff(438,plain,
% 3.48/2.49 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(439,plain,
% 3.48/2.49 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.48/2.49 inference(quant_inst,[status(thm)],[])).
% 3.48/2.49 tff(440,plain,
% 3.48/2.49 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.48/2.49 inference(modus_ponens,[status(thm)],[439, 438])).
% 3.48/2.49 tff(441,plain,
% 3.48/2.49 (v1_relat_1(k1_tsp_2(A!0, B!1))),
% 3.48/2.49 inference(unit_resolution,[status(thm)],[440, 437, 427])).
% 3.48/2.49 tff(442,plain,
% 3.48/2.49 (^[A: $i, B: $i] : refl((r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(443,plain,
% 3.48/2.49 (![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[442])).
% 3.48/2.49 tff(444,plain,
% 3.48/2.49 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(B) & v1_funct_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_funct_1(B))))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B))))), (((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> (((~v1_relat_1(B)) | (~v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)))), rewrite((((~v1_relat_1(B)) | (~v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))), (((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 3.48/2.49 inference(bind,[status(th)],[])).
% 3.48/2.49 tff(445,plain,
% 3.48/2.49 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.48/2.49 inference(quant_intro,[status(thm)],[444])).
% 3.48/2.49 tff(446,plain,
% 3.48/2.49 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 3.48/2.49 inference(rewrite,[status(thm)],[])).
% 3.48/2.49 tff(447,plain,
% 3.48/2.49 (^[A: $i, B: $i] : rewrite(((v1_relat_1(B) & v1_funct_1(B)) => r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)))),
% 3.51/2.50 inference(bind,[status(th)],[])).
% 3.51/2.50 tff(448,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 3.51/2.50 inference(quant_intro,[status(thm)],[447])).
% 3.51/2.50 tff(449,axiom,(![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t145_funct_1')).
% 3.51/2.50 tff(450,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[449, 448])).
% 3.51/2.50 tff(451,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[450, 446])).
% 3.51/2.50 tff(452,plain,(
% 3.51/2.50 ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 3.51/2.50 inference(skolemize,[status(sab)],[451])).
% 3.51/2.50 tff(453,plain,
% 3.51/2.50 (![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[452, 445])).
% 3.51/2.50 tff(454,plain,
% 3.51/2.50 (![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[453, 443])).
% 3.51/2.50 tff(455,plain,
% 3.51/2.50 (((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(456,plain,
% 3.51/2.50 ((r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1)))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(457,plain,
% 3.51/2.50 (((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 3.51/2.50 inference(monotonicity,[status(thm)],[456])).
% 3.51/2.50 tff(458,plain,
% 3.51/2.50 (((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.50 inference(transitivity,[status(thm)],[457, 455])).
% 3.51/2.50 tff(459,plain,
% 3.51/2.50 ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.50 inference(quant_inst,[status(thm)],[])).
% 3.51/2.50 tff(460,plain,
% 3.51/2.50 ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1)))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[459, 458])).
% 3.51/2.50 tff(461,plain,
% 3.51/2.50 (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.50 inference(unit_resolution,[status(thm)],[460, 454, 155, 441])).
% 3.51/2.50 tff(462,plain,
% 3.51/2.50 (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[461, 413])).
% 3.51/2.50 tff(463,plain,
% 3.51/2.50 ((~(r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))))) | (~r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))) | ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 3.51/2.50 inference(tautology,[status(thm)],[])).
% 3.51/2.50 tff(464,plain,
% 3.51/2.50 ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.50 inference(unit_resolution,[status(thm)],[463, 462, 254])).
% 3.51/2.50 tff(465,plain,
% 3.51/2.50 ((k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) <=> (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.50 inference(commutativity,[status(thm)],[])).
% 3.51/2.50 tff(466,plain,
% 3.51/2.50 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 3.51/2.50 inference(bind,[status(th)],[])).
% 3.51/2.50 tff(467,plain,
% 3.51/2.50 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.51/2.50 inference(quant_intro,[status(thm)],[466])).
% 3.51/2.50 tff(468,plain,
% 3.51/2.50 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 3.51/2.50 inference(bind,[status(th)],[])).
% 3.51/2.50 tff(469,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.51/2.50 inference(quant_intro,[status(thm)],[468])).
% 3.51/2.50 tff(470,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(471,plain,
% 3.51/2.50 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(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)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), trans(monotonicity(rewrite(((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) <=> (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B))), ((((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.51/2.50 inference(bind,[status(th)],[])).
% 3.51/2.50 tff(472,plain,
% 3.51/2.50 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(quant_intro,[status(thm)],[471])).
% 3.51/2.50 tff(473,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_tsp_2')).
% 3.51/2.50 tff(474,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[473, 472])).
% 3.51/2.50 tff(475,plain,
% 3.51/2.50 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[474, 470])).
% 3.51/2.50 tff(476,plain,(
% 3.51/2.50 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(skolemize,[status(sab)],[475])).
% 3.51/2.50 tff(477,plain,
% 3.51/2.50 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[476, 469])).
% 3.51/2.50 tff(478,plain,
% 3.51/2.50 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[477, 467])).
% 3.51/2.50 tff(479,plain,
% 3.51/2.50 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(480,plain,
% 3.51/2.50 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(481,plain,
% 3.51/2.50 ((~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(482,plain,
% 3.51/2.50 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.51/2.50 inference(monotonicity,[status(thm)],[481])).
% 3.51/2.50 tff(483,plain,
% 3.51/2.50 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.51/2.50 inference(transitivity,[status(thm)],[482, 480])).
% 3.51/2.50 tff(484,plain,
% 3.51/2.50 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 3.51/2.50 inference(monotonicity,[status(thm)],[483])).
% 3.51/2.50 tff(485,plain,
% 3.51/2.50 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.51/2.50 inference(transitivity,[status(thm)],[484, 479])).
% 3.51/2.50 tff(486,plain,
% 3.51/2.50 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 3.51/2.50 inference(quant_inst,[status(thm)],[])).
% 3.51/2.50 tff(487,plain,
% 3.51/2.50 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[486, 485])).
% 3.51/2.50 tff(488,plain,
% 3.51/2.50 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 3.51/2.50 inference(unit_resolution,[status(thm)],[487, 138, 137, 30, 95, 136, 478])).
% 3.51/2.50 tff(489,plain,
% 3.51/2.50 (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.51/2.50 inference(unit_resolution,[status(thm)],[488, 122])).
% 3.51/2.50 tff(490,plain,
% 3.51/2.50 (((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k3_tsp_2(A!0, B!1))),
% 3.51/2.50 inference(tautology,[status(thm)],[])).
% 3.51/2.50 tff(491,plain,
% 3.51/2.50 (v1_funct_1(k3_tsp_2(A!0, B!1))),
% 3.51/2.50 inference(unit_resolution,[status(thm)],[490, 489])).
% 3.51/2.50 tff(492,plain,
% 3.51/2.50 (((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.51/2.50 inference(tautology,[status(thm)],[])).
% 3.51/2.50 tff(493,plain,
% 3.51/2.50 (v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.51/2.50 inference(unit_resolution,[status(thm)],[492, 489])).
% 3.51/2.50 tff(494,plain,
% 3.51/2.50 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.51/2.50 inference(monotonicity,[status(thm)],[242])).
% 3.51/2.50 tff(495,plain,
% 3.51/2.50 (m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.51/2.50 inference(modus_ponens,[status(thm)],[269, 494])).
% 3.51/2.50 tff(496,plain,
% 3.51/2.50 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))),
% 3.51/2.50 inference(bind,[status(th)],[])).
% 3.51/2.50 tff(497,plain,
% 3.51/2.50 (![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(quant_intro,[status(thm)],[496])).
% 3.51/2.50 tff(498,plain,
% 3.51/2.50 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> (((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))))), rewrite((((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 3.51/2.50 inference(bind,[status(th)],[])).
% 3.51/2.50 tff(499,plain,
% 3.51/2.50 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.50 inference(quant_intro,[status(thm)],[498])).
% 3.51/2.50 tff(500,plain,
% 3.51/2.50 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 3.51/2.50 inference(rewrite,[status(thm)],[])).
% 3.51/2.50 tff(501,plain,
% 3.51/2.50 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))))),
% 3.51/2.51 inference(bind,[status(th)],[])).
% 3.51/2.51 tff(502,plain,
% 3.51/2.51 (![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 3.51/2.51 inference(quant_intro,[status(thm)],[501])).
% 3.51/2.51 tff(503,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_pre_topc')).
% 3.51/2.51 tff(504,plain,
% 3.51/2.51 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[503, 502])).
% 3.51/2.51 tff(505,plain,
% 3.51/2.51 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[504, 500])).
% 3.51/2.51 tff(506,plain,(
% 3.51/2.51 ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 3.51/2.51 inference(skolemize,[status(sab)],[505])).
% 3.51/2.51 tff(507,plain,
% 3.51/2.51 (![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[506, 499])).
% 3.51/2.51 tff(508,plain,
% 3.51/2.51 (![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[507, 497])).
% 3.51/2.51 tff(509,plain,
% 3.51/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(510,plain,
% 3.51/2.51 (((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(511,plain,
% 3.51/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[510])).
% 3.51/2.51 tff(512,plain,
% 3.51/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 3.51/2.51 inference(transitivity,[status(thm)],[511, 509])).
% 3.51/2.51 tff(513,plain,
% 3.51/2.51 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.51/2.51 inference(quant_inst,[status(thm)],[])).
% 3.51/2.51 tff(514,plain,
% 3.51/2.51 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[513, 512])).
% 3.51/2.51 tff(515,plain,
% 3.51/2.51 ((~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[514, 508, 34])).
% 3.51/2.51 tff(516,plain,
% 3.51/2.51 (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[515, 495, 493, 491, 74])).
% 3.51/2.51 tff(517,plain,
% 3.51/2.51 (r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))) <=> r2_hidden(C!2, u1_struct_0(A!0))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[162])).
% 3.51/2.51 tff(518,plain,
% 3.51/2.51 (r2_hidden(C!2, u1_struct_0(A!0)) <=> r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 3.51/2.51 inference(symmetry,[status(thm)],[517])).
% 3.51/2.51 tff(519,plain,
% 3.51/2.51 (^[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))))),
% 3.51/2.51 inference(bind,[status(th)],[])).
% 3.51/2.51 tff(520,plain,
% 3.51/2.51 (![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)))),
% 3.51/2.51 inference(quant_intro,[status(thm)],[519])).
% 3.51/2.51 tff(521,plain,
% 3.51/2.51 (![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)))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(522,plain,
% 3.51/2.51 (^[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))))),
% 3.51/2.51 inference(bind,[status(th)],[])).
% 3.51/2.51 tff(523,plain,
% 3.51/2.51 (![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)))),
% 3.51/2.51 inference(quant_intro,[status(thm)],[522])).
% 3.51/2.51 tff(524,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')).
% 3.51/2.51 tff(525,plain,
% 3.51/2.51 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[524, 523])).
% 3.51/2.51 tff(526,plain,
% 3.51/2.51 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[525, 521])).
% 3.51/2.51 tff(527,plain,(
% 3.51/2.51 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 3.51/2.51 inference(skolemize,[status(sab)],[526])).
% 3.51/2.51 tff(528,plain,
% 3.51/2.51 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[527, 520])).
% 3.51/2.51 tff(529,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(530,plain,
% 3.51/2.51 ((r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(531,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0))))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[530])).
% 3.51/2.51 tff(532,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))),
% 3.51/2.51 inference(transitivity,[status(thm)],[531, 529])).
% 3.51/2.51 tff(533,plain,
% 3.51/2.51 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.51/2.51 inference(quant_inst,[status(thm)],[])).
% 3.51/2.51 tff(534,plain,
% 3.51/2.51 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[533, 532])).
% 3.51/2.51 tff(535,plain,
% 3.51/2.51 (v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0))),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[534, 188, 528])).
% 3.51/2.51 tff(536,plain,
% 3.51/2.51 (r2_hidden(C!2, u1_struct_0(A!0))),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[535, 290])).
% 3.51/2.51 tff(537,plain,
% 3.51/2.51 (r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[536, 518])).
% 3.51/2.51 tff(538,plain,
% 3.51/2.51 (^[A: $i, B: $i] : refl(((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B))))),
% 3.51/2.51 inference(bind,[status(th)],[])).
% 3.51/2.51 tff(539,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.51/2.51 inference(quant_intro,[status(thm)],[538])).
% 3.51/2.51 tff(540,plain,
% 3.51/2.51 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(B) & v1_funct_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_funct_1(B))))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B))))), (((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | ((~v1_relat_1(B)) | (~v1_funct_1(B)))))), rewrite(((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | ((~v1_relat_1(B)) | (~v1_funct_1(B)))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))), (((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 3.51/2.51 inference(bind,[status(th)],[])).
% 3.51/2.51 tff(541,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.51/2.51 inference(quant_intro,[status(thm)],[540])).
% 3.51/2.51 tff(542,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(543,plain,
% 3.51/2.51 (^[A: $i, B: $i] : trans(monotonicity(rewrite((r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A)))) <=> ((~r2_hidden(A, k1_relat_1(B))) | (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))), (((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ((v1_relat_1(B) & v1_funct_1(B)) => ((~r2_hidden(A, k1_relat_1(B))) | (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))))), rewrite(((v1_relat_1(B) & v1_funct_1(B)) => ((~r2_hidden(A, k1_relat_1(B))) | (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))), (((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))))),
% 3.51/2.51 inference(bind,[status(th)],[])).
% 3.51/2.51 tff(544,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 3.51/2.51 inference(quant_intro,[status(thm)],[543])).
% 3.51/2.51 tff(545,axiom,(![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t117_funct_1')).
% 3.51/2.51 tff(546,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[545, 544])).
% 3.51/2.51 tff(547,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[546, 542])).
% 3.51/2.51 tff(548,plain,(
% 3.51/2.51 ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 3.51/2.51 inference(skolemize,[status(sab)],[547])).
% 3.51/2.51 tff(549,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[548, 541])).
% 3.51/2.51 tff(550,plain,
% 3.51/2.51 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[549, 539])).
% 3.51/2.51 tff(551,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(552,plain,
% 3.51/2.51 (((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1)))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(553,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))))))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[552])).
% 3.51/2.51 tff(554,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 3.51/2.51 inference(transitivity,[status(thm)],[553, 551])).
% 3.51/2.51 tff(555,plain,
% 3.51/2.51 ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.51 inference(quant_inst,[status(thm)],[])).
% 3.51/2.51 tff(556,plain,
% 3.51/2.51 ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[555, 554])).
% 3.51/2.51 tff(557,plain,
% 3.51/2.51 ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))))),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[556, 550, 155, 441])).
% 3.51/2.51 tff(558,plain,
% 3.51/2.51 (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[557, 537])).
% 3.51/2.51 tff(559,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(560,plain,
% 3.51/2.51 ((v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(561,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2))))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[560])).
% 3.51/2.51 tff(562,plain,
% 3.51/2.51 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))),
% 3.51/2.51 inference(transitivity,[status(thm)],[561, 559])).
% 3.51/2.51 tff(563,plain,
% 3.51/2.51 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.51/2.51 inference(quant_inst,[status(thm)],[])).
% 3.51/2.51 tff(564,plain,
% 3.51/2.51 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2))),
% 3.51/2.51 inference(modus_ponens,[status(thm)],[563, 562])).
% 3.51/2.51 tff(565,plain,
% 3.51/2.51 (k1_struct_0(A!0, C!2) = k1_tarski(C!2)),
% 3.51/2.51 inference(unit_resolution,[status(thm)],[564, 138, 188, 324, 34])).
% 3.51/2.51 tff(566,plain,
% 3.51/2.51 (k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[241, 565])).
% 3.51/2.51 tff(567,plain,
% 3.51/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(568,plain,
% 3.51/2.51 (((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))),
% 3.51/2.51 inference(rewrite,[status(thm)],[])).
% 3.51/2.51 tff(569,plain,
% 3.51/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)))))),
% 3.51/2.51 inference(monotonicity,[status(thm)],[568])).
% 3.51/2.51 tff(570,plain,
% 3.51/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))),
% 3.51/2.51 inference(transitivity,[status(thm)],[569, 567])).
% 3.51/2.51 tff(571,plain,
% 3.51/2.51 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 3.51/2.51 inference(quant_inst,[status(thm)],[])).
% 3.51/2.51 tff(572,plain,
% 3.51/2.51 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[571, 570])).
% 3.51/2.52 tff(573,plain,
% 3.51/2.52 ((~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)))),
% 3.51/2.52 inference(unit_resolution,[status(thm)],[572, 508, 34])).
% 3.51/2.52 tff(574,plain,
% 3.51/2.52 (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))),
% 3.51/2.52 inference(unit_resolution,[status(thm)],[573, 495, 493, 491, 74])).
% 3.51/2.52 tff(575,plain,
% 3.51/2.52 (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))),
% 3.51/2.52 inference(transitivity,[status(thm)],[574, 566, 558])).
% 3.51/2.52 tff(576,plain,
% 3.51/2.52 ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) <=> (k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 3.51/2.52 inference(monotonicity,[status(thm)],[575, 516])).
% 3.51/2.52 tff(577,plain,
% 3.51/2.52 ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) <=> (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.52 inference(transitivity,[status(thm)],[576, 465])).
% 3.51/2.52 tff(578,plain,
% 3.51/2.52 ((~(k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))) <=> (~(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 3.51/2.52 inference(monotonicity,[status(thm)],[577])).
% 3.51/2.52 tff(579,plain,
% 3.51/2.52 (~(k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 3.51/2.52 inference(or_elim,[status(thm)],[187])).
% 3.51/2.52 tff(580,plain,
% 3.51/2.52 (~(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[579, 578])).
% 3.51/2.52 tff(581,plain,
% 3.51/2.52 ((~((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 3.51/2.52 inference(tautology,[status(thm)],[])).
% 3.51/2.52 tff(582,plain,
% 3.51/2.52 (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0),
% 3.51/2.52 inference(unit_resolution,[status(thm)],[581, 580, 464])).
% 3.51/2.52 tff(583,plain,
% 3.51/2.52 (k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[582, 245])).
% 3.51/2.52 tff(584,plain,
% 3.51/2.52 (^[A: $i, B: $i] : refl(((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))) <=> ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))),
% 3.51/2.52 inference(bind,[status(th)],[])).
% 3.51/2.52 tff(585,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))) <=> ![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 3.51/2.52 inference(quant_intro,[status(thm)],[584])).
% 3.51/2.52 tff(586,plain,
% 3.51/2.52 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)) <=> (~((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))), ((~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))) <=> (~(~((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))))), rewrite((~(~((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))) <=> ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))), ((~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))) <=> ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))), (((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((~v1_relat_1(B)) | ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))))), rewrite(((~v1_relat_1(B)) | ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) <=> ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))), (((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))))),
% 3.51/2.52 inference(bind,[status(th)],[])).
% 3.51/2.52 tff(587,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 3.51/2.52 inference(quant_intro,[status(thm)],[586])).
% 3.51/2.52 tff(588,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(589,plain,
% 3.51/2.52 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0))) <=> (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))), ((v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> (v1_relat_1(B) => (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))))), rewrite((v1_relat_1(B) => (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))), ((v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))))),
% 3.51/2.52 inference(bind,[status(th)],[])).
% 3.51/2.52 tff(590,plain,
% 3.51/2.52 (![A: $i, B: $i] : (v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 3.51/2.52 inference(quant_intro,[status(thm)],[589])).
% 3.51/2.52 tff(591,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t152_relat_1')).
% 3.51/2.52 tff(592,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[591, 590])).
% 3.51/2.52 tff(593,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[592, 588])).
% 3.51/2.52 tff(594,plain,(
% 3.51/2.52 ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 3.51/2.52 inference(skolemize,[status(sab)],[593])).
% 3.51/2.52 tff(595,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[594, 587])).
% 3.51/2.52 tff(596,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[595, 585])).
% 3.51/2.52 tff(597,plain,
% 3.51/2.52 (((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))) <=> ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(598,plain,
% 3.51/2.52 (((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))) <=> ((~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(599,plain,
% 3.51/2.52 (((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))) <=> ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))))),
% 3.51/2.52 inference(monotonicity,[status(thm)],[598])).
% 3.51/2.52 tff(600,plain,
% 3.51/2.52 (((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))) <=> ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 3.51/2.52 inference(transitivity,[status(thm)],[599, 597])).
% 3.51/2.52 tff(601,plain,
% 3.51/2.52 ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 3.51/2.52 inference(quant_inst,[status(thm)],[])).
% 3.51/2.52 tff(602,plain,
% 3.51/2.52 ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[601, 600])).
% 3.51/2.52 tff(603,plain,
% 3.51/2.52 ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))),
% 3.51/2.52 inference(unit_resolution,[status(thm)],[602, 596, 441])).
% 3.51/2.52 tff(604,plain,
% 3.51/2.52 (k2_tex_4(A!0, C!2) = k1_xboole_0),
% 3.51/2.52 inference(unit_resolution,[status(thm)],[603, 583, 199])).
% 3.51/2.52 tff(605,plain,
% 3.51/2.52 (k4_tex_4(A!0, C!2) = k1_xboole_0),
% 3.51/2.52 inference(transitivity,[status(thm)],[219, 604])).
% 3.51/2.52 tff(606,plain,
% 3.51/2.52 (v1_xboole_0(k4_tex_4(A!0, C!2)) <=> v1_xboole_0(k1_xboole_0)),
% 3.51/2.52 inference(monotonicity,[status(thm)],[605])).
% 3.51/2.52 tff(607,plain,
% 3.51/2.52 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k4_tex_4(A!0, C!2))),
% 3.51/2.52 inference(symmetry,[status(thm)],[606])).
% 3.51/2.52 tff(608,plain,
% 3.51/2.52 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(609,axiom,(((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)) & v5_membered(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_membered')).
% 3.51/2.52 tff(610,plain,
% 3.51/2.52 ((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)),
% 3.51/2.52 inference(and_elim,[status(thm)],[609])).
% 3.51/2.52 tff(611,plain,
% 3.51/2.52 (((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)),
% 3.51/2.52 inference(and_elim,[status(thm)],[610])).
% 3.51/2.52 tff(612,plain,
% 3.51/2.52 ((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)),
% 3.51/2.52 inference(and_elim,[status(thm)],[611])).
% 3.51/2.52 tff(613,plain,
% 3.51/2.52 (v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)),
% 3.51/2.52 inference(and_elim,[status(thm)],[612])).
% 3.51/2.52 tff(614,plain,
% 3.51/2.52 (v1_xboole_0(k1_xboole_0)),
% 3.51/2.52 inference(and_elim,[status(thm)],[613])).
% 3.51/2.52 tff(615,plain,
% 3.51/2.52 (v1_xboole_0(k1_xboole_0)),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[614, 608])).
% 3.51/2.52 tff(616,plain,
% 3.51/2.52 (v1_xboole_0(k4_tex_4(A!0, C!2))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[615, 607])).
% 3.51/2.52 tff(617,plain,
% 3.51/2.52 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))))),
% 3.51/2.52 inference(bind,[status(th)],[])).
% 3.51/2.52 tff(618,plain,
% 3.51/2.52 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 3.51/2.52 inference(quant_intro,[status(thm)],[617])).
% 3.51/2.52 tff(619,plain,
% 3.51/2.52 (^[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))) | (~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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite(((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 3.51/2.52 inference(bind,[status(th)],[])).
% 3.51/2.52 tff(620,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 3.51/2.52 inference(quant_intro,[status(thm)],[619])).
% 3.51/2.52 tff(621,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(622,plain,
% 3.51/2.52 (^[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))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(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))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 3.51/2.52 inference(bind,[status(th)],[])).
% 3.51/2.52 tff(623,plain,
% 3.51/2.52 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 3.51/2.52 inference(quant_intro,[status(thm)],[622])).
% 3.51/2.52 tff(624,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))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_tex_4')).
% 3.51/2.52 tff(625,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[624, 623])).
% 3.51/2.52 tff(626,plain,
% 3.51/2.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[625, 621])).
% 3.51/2.52 tff(627,plain,(
% 3.51/2.52 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 3.51/2.52 inference(skolemize,[status(sab)],[626])).
% 3.51/2.52 tff(628,plain,
% 3.51/2.52 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[627, 620])).
% 3.51/2.52 tff(629,plain,
% 3.51/2.52 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 3.51/2.52 inference(modus_ponens,[status(thm)],[628, 618])).
% 3.51/2.52 tff(630,plain,
% 3.51/2.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(631,plain,
% 3.51/2.52 ((v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 3.51/2.52 inference(rewrite,[status(thm)],[])).
% 3.51/2.52 tff(632,plain,
% 3.51/2.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 3.54/2.53 inference(monotonicity,[status(thm)],[631])).
% 3.54/2.53 tff(633,plain,
% 3.54/2.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 3.54/2.53 inference(transitivity,[status(thm)],[632, 630])).
% 3.54/2.53 tff(634,plain,
% 3.54/2.53 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 3.54/2.53 inference(quant_inst,[status(thm)],[])).
% 3.54/2.53 tff(635,plain,
% 3.54/2.53 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 3.54/2.53 inference(modus_ponens,[status(thm)],[634, 633])).
% 3.54/2.53 tff(636,plain,
% 3.54/2.53 (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 3.54/2.53 inference(unit_resolution,[status(thm)],[635, 138, 137, 30, 188, 629])).
% 3.54/2.53 tff(637,plain,
% 3.54/2.53 ((v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) | (~v1_xboole_0(k4_tex_4(A!0, C!2)))),
% 3.54/2.53 inference(tautology,[status(thm)],[])).
% 3.54/2.53 tff(638,plain,
% 3.54/2.53 (~v1_xboole_0(k4_tex_4(A!0, C!2))),
% 3.54/2.53 inference(unit_resolution,[status(thm)],[637, 636])).
% 3.54/2.53 tff(639,plain,
% 3.54/2.53 ($false),
% 3.54/2.53 inference(unit_resolution,[status(thm)],[638, 616])).
% 3.54/2.53 % SZS output end Proof
%------------------------------------------------------------------------------