Z3---4.15.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : TOP041+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:42:42 AM UTC 2025

% Result   : Theorem 1.39s 1.54s
% Output   : Proof 1.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : TOP041+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri Jun 20 14:01:40 EDT 2025
% 0.14/0.36  % CPUTime    : 
% 1.39/1.54  % SZS status Theorem
% 1.39/1.54  % SZS output start Proof
% 1.39/1.54  tff(k3_xboole_0_type, type, (
% 1.39/1.54     k3_xboole_0: ( $i * $i ) > $i)).
% 1.39/1.54  tff(u1_struct_0_type, type, (
% 1.39/1.54     u1_struct_0: $i > $i)).
% 1.39/1.54  tff(tptp_fun_B_1_type, type, (
% 1.39/1.54     tptp_fun_B_1: $i)).
% 1.39/1.54  tff(tptp_fun_C_2_type, type, (
% 1.39/1.54     tptp_fun_C_2: $i)).
% 1.39/1.54  tff(k4_pre_topc_type, type, (
% 1.39/1.54     k4_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 1.39/1.54  tff(k4_tsp_2_type, type, (
% 1.39/1.54     k4_tsp_2: ( $i * $i ) > $i)).
% 1.39/1.54  tff(tptp_fun_A_0_type, type, (
% 1.39/1.54     tptp_fun_A_0: $i)).
% 1.39/1.54  tff(k5_subset_1_type, type, (
% 1.39/1.54     k5_subset_1: ( $i * $i * $i ) > $i)).
% 1.39/1.54  tff(m1_subset_1_type, type, (
% 1.39/1.54     m1_subset_1: ( $i * $i ) > $o)).
% 1.39/1.54  tff(k1_zfmisc_1_type, type, (
% 1.39/1.54     k1_zfmisc_1: $i > $i)).
% 1.39/1.54  tff(m1_pre_topc_type, type, (
% 1.39/1.54     m1_pre_topc: ( $i * $i ) > $o)).
% 1.39/1.54  tff(m2_tsp_1_type, type, (
% 1.39/1.54     m2_tsp_1: ( $i * $i ) > $o)).
% 1.39/1.54  tff(l1_pre_topc_type, type, (
% 1.39/1.54     l1_pre_topc: $i > $o)).
% 1.39/1.54  tff(v3_pre_topc_type, type, (
% 1.39/1.54     v3_pre_topc: ( $i * $i ) > $o)).
% 1.39/1.54  tff(v2_tsp_2_type, type, (
% 1.39/1.54     v2_tsp_2: ( $i * $i ) > $o)).
% 1.39/1.54  tff(v3_struct_0_type, type, (
% 1.39/1.54     v3_struct_0: $i > $o)).
% 1.39/1.54  tff(v2_pre_topc_type, type, (
% 1.39/1.54     v2_pre_topc: $i > $o)).
% 1.39/1.54  tff(k3_tex_4_type, type, (
% 1.39/1.54     k3_tex_4: ( $i * $i ) > $i)).
% 1.39/1.54  tff(k1_tsp_2_type, type, (
% 1.39/1.54     k1_tsp_2: ( $i * $i ) > $i)).
% 1.39/1.54  tff(tptp_fun_E_3_type, type, (
% 1.39/1.54     tptp_fun_E_3: ( $i * $i * $i ) > $i)).
% 1.39/1.54  tff(m2_relset_1_type, type, (
% 1.39/1.54     m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.39/1.54  tff(v5_pre_topc_type, type, (
% 1.39/1.54     v5_pre_topc: ( $i * $i * $i ) > $o)).
% 1.39/1.54  tff(v1_funct_2_type, type, (
% 1.39/1.54     v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.39/1.54  tff(v1_funct_1_type, type, (
% 1.39/1.54     v1_funct_1: $i > $o)).
% 1.39/1.54  tff(tptp_fun_D_4_type, type, (
% 1.39/1.54     tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 1.39/1.54  tff(l1_struct_0_type, type, (
% 1.39/1.54     l1_struct_0: $i > $o)).
% 1.39/1.54  tff(m1_relset_1_type, type, (
% 1.39/1.54     m1_relset_1: ( $i * $i * $i ) > $o)).
% 1.39/1.54  tff(r1_tarski_type, type, (
% 1.39/1.54     r1_tarski: ( $i * $i ) > $o)).
% 1.39/1.54  tff(m1_tsp_1_type, type, (
% 1.39/1.54     m1_tsp_1: ( $i * $i ) > $o)).
% 1.39/1.54  tff(tptp_fun_D_6_type, type, (
% 1.39/1.54     tptp_fun_D_6: ( $i * $i ) > $i)).
% 1.39/1.54  tff(tptp_fun_C_5_type, type, (
% 1.39/1.54     tptp_fun_C_5: ( $i * $i ) > $i)).
% 1.39/1.54  tff(1,plain,
% 1.39/1.54      (^[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))))),
% 1.39/1.54      inference(bind,[status(th)],[])).
% 1.39/1.54  tff(2,plain,
% 1.39/1.54      (![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)))),
% 1.39/1.54      inference(quant_intro,[status(thm)],[1])).
% 1.39/1.54  tff(3,plain,
% 1.39/1.54      (^[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))))),
% 1.39/1.54      inference(bind,[status(th)],[])).
% 1.39/1.54  tff(4,plain,
% 1.39/1.54      (![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)))),
% 1.39/1.54      inference(quant_intro,[status(thm)],[3])).
% 1.39/1.54  tff(5,plain,
% 1.39/1.54      (![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)))),
% 1.39/1.54      inference(transitivity,[status(thm)],[4, 2])).
% 1.39/1.54  tff(6,plain,
% 1.39/1.54      (![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)))),
% 1.39/1.54      inference(rewrite,[status(thm)],[])).
% 1.39/1.54  tff(7,plain,
% 1.39/1.54      (^[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))))),
% 1.39/1.54      inference(bind,[status(th)],[])).
% 1.39/1.54  tff(8,plain,
% 1.39/1.54      (![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)))),
% 1.39/1.54      inference(quant_intro,[status(thm)],[7])).
% 1.39/1.54  tff(9,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')).
% 1.39/1.54  tff(10,plain,
% 1.39/1.54      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[9, 8])).
% 1.39/1.55  tff(11,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[10, 6])).
% 1.39/1.55  tff(12,plain,(
% 1.39/1.55      ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.39/1.55      inference(skolemize,[status(sab)],[11])).
% 1.39/1.55  tff(13,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[12, 5])).
% 1.39/1.55  tff(14,plain,
% 1.39/1.55      ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(15,plain,
% 1.39/1.55      ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(16,plain,
% 1.39/1.55      ((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(17,plain,
% 1.39/1.55      ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 1.39/1.55      inference(monotonicity,[status(thm)],[16])).
% 1.39/1.55  tff(18,plain,
% 1.39/1.55      ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 1.39/1.55      inference(transitivity,[status(thm)],[17, 15])).
% 1.39/1.55  tff(19,plain,
% 1.39/1.55      ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 1.39/1.55      inference(monotonicity,[status(thm)],[18])).
% 1.39/1.55  tff(20,plain,
% 1.39/1.55      ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 1.39/1.55      inference(transitivity,[status(thm)],[19, 14])).
% 1.39/1.55  tff(21,plain,
% 1.39/1.55      ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(22,plain,
% 1.39/1.55      ((~![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, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(23,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, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(C, A) => v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_tsp_2')).
% 1.39/1.55  tff(24,plain,
% 1.39/1.55      (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[23, 22])).
% 1.39/1.55  tff(25,plain,
% 1.39/1.55      (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[24, 21])).
% 1.39/1.55  tff(26,plain,
% 1.39/1.55      (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[25, 21])).
% 1.39/1.55  tff(27,plain,
% 1.39/1.55      (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v3_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[26, 21])).
% 1.39/1.55  tff(28,plain,
% 1.39/1.55      ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[27, 20])).
% 1.39/1.55  tff(29,plain,
% 1.39/1.55      (l1_pre_topc(A!0)),
% 1.39/1.55      inference(and_elim,[status(thm)],[28])).
% 1.39/1.55  tff(30,plain,
% 1.39/1.55      (((~![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)))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(31,plain,
% 1.39/1.55      ((~![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)))),
% 1.39/1.55      inference(quant_inst,[status(thm)],[])).
% 1.39/1.55  tff(32,plain,
% 1.39/1.55      ((~![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))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[31, 30])).
% 1.39/1.55  tff(33,plain,
% 1.39/1.55      (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[32, 29, 13])).
% 1.39/1.55  tff(34,plain,
% 1.39/1.55      ((~![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))),
% 1.39/1.55      inference(quant_inst,[status(thm)],[])).
% 1.39/1.55  tff(35,plain,
% 1.39/1.55      (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[34, 33])).
% 1.39/1.55  tff(36,plain,
% 1.39/1.55      (m2_tsp_1(B!1, A!0)),
% 1.39/1.55      inference(and_elim,[status(thm)],[28])).
% 1.39/1.55  tff(37,plain,
% 1.39/1.55      ((~(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)),
% 1.39/1.55      inference(tautology,[status(thm)],[])).
% 1.39/1.55  tff(38,plain,
% 1.39/1.55      ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[37, 36])).
% 1.39/1.55  tff(39,plain,
% 1.39/1.55      (m1_pre_topc(B!1, A!0)),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[38, 35])).
% 1.39/1.55  tff(40,plain,
% 1.39/1.55      (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(41,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[40])).
% 1.39/1.55  tff(42,plain,
% 1.39/1.55      (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(43,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[42])).
% 1.39/1.55  tff(44,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(transitivity,[status(thm)],[43, 41])).
% 1.39/1.55  tff(45,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(46,plain,
% 1.39/1.55      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(47,plain,
% 1.39/1.55      (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[46])).
% 1.39/1.55  tff(48,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_tsep_1')).
% 1.39/1.55  tff(49,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[48, 47])).
% 1.39/1.55  tff(50,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[49, 45])).
% 1.39/1.55  tff(51,plain,(
% 1.39/1.55      ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(skolemize,[status(sab)],[50])).
% 1.39/1.55  tff(52,plain,
% 1.39/1.55      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[51, 44])).
% 1.39/1.55  tff(53,plain,
% 1.39/1.55      (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(54,plain,
% 1.39/1.55      ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.39/1.55      inference(quant_inst,[status(thm)],[])).
% 1.39/1.55  tff(55,plain,
% 1.39/1.55      ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[54, 53])).
% 1.39/1.55  tff(56,plain,
% 1.39/1.55      (![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[55, 29, 52])).
% 1.39/1.55  tff(57,plain,
% 1.39/1.55      (((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(58,plain,
% 1.39/1.55      ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.39/1.55      inference(quant_inst,[status(thm)],[])).
% 1.39/1.55  tff(59,plain,
% 1.39/1.55      ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[58, 57])).
% 1.39/1.55  tff(60,plain,
% 1.39/1.55      (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[59, 56, 39])).
% 1.39/1.55  tff(61,plain,
% 1.39/1.55      (^[A: $i, B: $i, C: $i] : refl(((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(62,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[61])).
% 1.39/1.55  tff(63,plain,
% 1.39/1.55      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(64,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[63])).
% 1.39/1.55  tff(65,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(66,plain,
% 1.39/1.55      (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(67,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[66])).
% 1.39/1.55  tff(68,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 1.39/1.55  tff(69,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[68, 67])).
% 1.39/1.55  tff(70,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[69, 65])).
% 1.39/1.55  tff(71,plain,(
% 1.39/1.55      ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 1.39/1.55      inference(skolemize,[status(sab)],[70])).
% 1.39/1.55  tff(72,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[71, 64])).
% 1.39/1.55  tff(73,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[72, 62])).
% 1.39/1.55  tff(74,plain,
% 1.39/1.55      (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.39/1.55      inference(and_elim,[status(thm)],[28])).
% 1.39/1.55  tff(75,plain,
% 1.39/1.55      (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.39/1.55      inference(or_elim,[status(thm)],[74])).
% 1.39/1.55  tff(76,plain,
% 1.39/1.55      (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(77,plain,
% 1.39/1.55      (((k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(78,plain,
% 1.39/1.55      (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1)))))),
% 1.39/1.55      inference(monotonicity,[status(thm)],[77])).
% 1.39/1.55  tff(79,plain,
% 1.39/1.55      (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))))),
% 1.39/1.55      inference(transitivity,[status(thm)],[78, 76])).
% 1.39/1.55  tff(80,plain,
% 1.39/1.55      ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.39/1.55      inference(quant_inst,[status(thm)],[])).
% 1.39/1.55  tff(81,plain,
% 1.39/1.55      ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[80, 79])).
% 1.39/1.55  tff(82,plain,
% 1.39/1.55      (k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)) = k3_xboole_0(C!2, u1_struct_0(B!1))),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[81, 75, 73, 60])).
% 1.39/1.55  tff(83,plain,
% 1.39/1.55      (^[A: $i, B: $i, C: $i] : refl(((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(84,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[83])).
% 1.39/1.55  tff(85,plain,
% 1.39/1.55      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(86,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[85])).
% 1.39/1.55  tff(87,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(88,plain,
% 1.39/1.55      (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(89,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k5_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[88])).
% 1.39/1.55  tff(90,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k5_subset_1')).
% 1.39/1.55  tff(91,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[90, 89])).
% 1.39/1.55  tff(92,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[91, 87])).
% 1.39/1.55  tff(93,plain,(
% 1.39/1.55      ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k5_subset_1(A, C, B)))),
% 1.39/1.55      inference(skolemize,[status(sab)],[92])).
% 1.39/1.55  tff(94,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[93, 86])).
% 1.39/1.55  tff(95,plain,
% 1.39/1.55      (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[94, 84])).
% 1.39/1.55  tff(96,plain,
% 1.39/1.55      (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(97,plain,
% 1.39/1.55      (((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))))),
% 1.39/1.55      inference(rewrite,[status(thm)],[])).
% 1.39/1.55  tff(98,plain,
% 1.39/1.55      (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)))))),
% 1.39/1.55      inference(monotonicity,[status(thm)],[97])).
% 1.39/1.55  tff(99,plain,
% 1.39/1.55      (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))))),
% 1.39/1.55      inference(transitivity,[status(thm)],[98, 96])).
% 1.39/1.55  tff(100,plain,
% 1.39/1.55      ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.39/1.55      inference(quant_inst,[status(thm)],[])).
% 1.39/1.55  tff(101,plain,
% 1.39/1.55      ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k5_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1)))),
% 1.39/1.55      inference(modus_ponens,[status(thm)],[100, 99])).
% 1.39/1.55  tff(102,plain,
% 1.39/1.55      (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), C!2, u1_struct_0(B!1))),
% 1.39/1.55      inference(unit_resolution,[status(thm)],[101, 75, 95, 60])).
% 1.39/1.55  tff(103,plain,
% 1.39/1.55      (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(104,plain,
% 1.39/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[103])).
% 1.39/1.55  tff(105,plain,
% 1.39/1.55      (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.39/1.55  tff(106,plain,
% 1.39/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.39/1.55      inference(quant_intro,[status(thm)],[105])).
% 1.39/1.55  tff(107,plain,
% 1.39/1.55      (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 1.39/1.55      inference(bind,[status(th)],[])).
% 1.41/1.55  tff(108,plain,
% 1.41/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.41/1.55      inference(quant_intro,[status(thm)],[107])).
% 1.41/1.55  tff(109,plain,
% 1.41/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.41/1.55      inference(transitivity,[status(thm)],[108, 106])).
% 1.41/1.55  tff(110,plain,
% 1.41/1.55      (^[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))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))))),
% 1.41/1.55      inference(bind,[status(th)],[])).
% 1.41/1.55  tff(111,plain,
% 1.41/1.55      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.41/1.55      inference(quant_intro,[status(thm)],[110])).
% 1.41/1.55  tff(112,plain,
% 1.41/1.55      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.41/1.55      inference(rewrite,[status(thm)],[])).
% 1.41/1.55  tff(113,plain,
% 1.41/1.55      (^[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_pre_topc(B, A) => (k3_tex_4(A, B) = B)) <=> ((~v3_pre_topc(B, A)) | (k3_tex_4(A, B) = B))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_pre_topc(B, A)) | (k3_tex_4(A, B) = B))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_pre_topc(B, A)) | (k3_tex_4(A, B) = B))) <=> ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))))),
% 1.41/1.55      inference(bind,[status(th)],[])).
% 1.41/1.55  tff(114,plain,
% 1.41/1.55      (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.41/1.55      inference(quant_intro,[status(thm)],[113])).
% 1.41/1.55  tff(115,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t58_tex_4')).
% 1.41/1.55  tff(116,plain,
% 1.41/1.55      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.41/1.55      inference(modus_ponens,[status(thm)],[115, 114])).
% 1.41/1.55  tff(117,plain,
% 1.41/1.55      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.41/1.55      inference(modus_ponens,[status(thm)],[116, 112])).
% 1.41/1.55  tff(118,plain,(
% 1.41/1.55      ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.41/1.55      inference(skolemize,[status(sab)],[117])).
% 1.41/1.55  tff(119,plain,
% 1.41/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.41/1.55      inference(modus_ponens,[status(thm)],[118, 111])).
% 1.41/1.55  tff(120,plain,
% 1.41/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.41/1.55      inference(modus_ponens,[status(thm)],[119, 109])).
% 1.41/1.55  tff(121,plain,
% 1.41/1.55      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 1.41/1.55      inference(modus_ponens,[status(thm)],[120, 104])).
% 1.41/1.55  tff(122,plain,
% 1.41/1.55      (v2_pre_topc(A!0)),
% 1.41/1.55      inference(and_elim,[status(thm)],[28])).
% 1.41/1.55  tff(123,plain,
% 1.41/1.55      (~v3_struct_0(A!0)),
% 1.41/1.55      inference(and_elim,[status(thm)],[28])).
% 1.41/1.55  tff(124,plain,
% 1.41/1.55      (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))),
% 1.41/1.56      inference(rewrite,[status(thm)],[])).
% 1.41/1.56  tff(125,plain,
% 1.41/1.56      ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0)))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))),
% 1.41/1.56      inference(rewrite,[status(thm)],[])).
% 1.41/1.56  tff(126,plain,
% 1.41/1.56      (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))))),
% 1.41/1.56      inference(monotonicity,[status(thm)],[125])).
% 1.41/1.56  tff(127,plain,
% 1.41/1.56      (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))),
% 1.41/1.56      inference(transitivity,[status(thm)],[126, 124])).
% 1.41/1.56  tff(128,plain,
% 1.41/1.56      ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0))))),
% 1.41/1.56      inference(quant_inst,[status(thm)],[])).
% 1.41/1.56  tff(129,plain,
% 1.41/1.56      ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))),
% 1.41/1.56      inference(modus_ponens,[status(thm)],[128, 127])).
% 1.41/1.56  tff(130,plain,
% 1.41/1.56      (![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))),
% 1.41/1.56      inference(unit_resolution,[status(thm)],[129, 123, 122, 29, 121])).
% 1.41/1.56  tff(131,plain,
% 1.41/1.56      (v3_pre_topc(C!2, A!0)),
% 1.41/1.56      inference(or_elim,[status(thm)],[74])).
% 1.41/1.56  tff(132,plain,
% 1.41/1.56      (((~![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | ((~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, C!2) = C!2))) <=> ((~![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, C!2) = C!2))),
% 1.41/1.56      inference(rewrite,[status(thm)],[])).
% 1.41/1.56  tff(133,plain,
% 1.41/1.56      ((~![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | ((~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, C!2) = C!2))),
% 1.41/1.56      inference(quant_inst,[status(thm)],[])).
% 1.41/1.56  tff(134,plain,
% 1.41/1.56      ((~![B: $i] : ((~v3_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, C!2) = C!2)),
% 1.41/1.56      inference(modus_ponens,[status(thm)],[133, 132])).
% 1.41/1.56  tff(135,plain,
% 1.41/1.56      (k3_tex_4(A!0, C!2) = C!2),
% 1.41/1.56      inference(unit_resolution,[status(thm)],[134, 131, 75, 130])).
% 1.41/1.56  tff(136,plain,
% 1.41/1.56      (C!2 = k3_tex_4(A!0, C!2)),
% 1.41/1.56      inference(symmetry,[status(thm)],[135])).
% 1.41/1.56  tff(137,plain,
% 1.41/1.56      (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2))),
% 1.41/1.56      inference(monotonicity,[status(thm)],[136])).
% 1.41/1.56  tff(138,plain,
% 1.41/1.56      (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2)) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2)),
% 1.41/1.56      inference(symmetry,[status(thm)],[137])).
% 1.41/1.56  tff(139,plain,
% 1.41/1.56      (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))))),
% 1.41/1.56      inference(bind,[status(th)],[])).
% 1.41/1.56  tff(140,plain,
% 1.41/1.56      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))),
% 1.41/1.56      inference(quant_intro,[status(thm)],[139])).
% 1.41/1.56  tff(141,plain,
% 1.41/1.56      (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))))),
% 1.41/1.56      inference(bind,[status(th)],[])).
% 1.41/1.56  tff(142,plain,
% 1.41/1.56      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))),
% 1.41/1.56      inference(quant_intro,[status(thm)],[141])).
% 1.41/1.56  tff(143,plain,
% 1.41/1.56      (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))))),
% 1.41/1.56      inference(bind,[status(th)],[])).
% 1.41/1.56  tff(144,plain,
% 1.41/1.56      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))),
% 1.41/1.56      inference(quant_intro,[status(thm)],[143])).
% 1.41/1.56  tff(145,plain,
% 1.41/1.56      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))),
% 1.41/1.56      inference(transitivity,[status(thm)],[144, 142])).
% 1.41/1.56  tff(146,plain,
% 1.41/1.56      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), trans(monotonicity(rewrite((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))), trans(monotonicity(rewrite(((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))), (((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))), rewrite(((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))) <=> ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))), (((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))), (((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))), rewrite(((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) <=> (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))), (((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))))),
% 1.41/1.56      inference(bind,[status(th)],[])).
% 1.41/1.56  tff(147,plain,
% 1.41/1.56      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))),
% 1.41/1.56      inference(quant_intro,[status(thm)],[146])).
% 1.41/1.56  tff(148,plain,
% 1.41/1.56      (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))))),
% 1.41/1.56      inference(bind,[status(th)],[])).
% 1.41/1.56  tff(149,plain,
% 1.41/1.56      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.56      inference(quant_intro,[status(thm)],[148])).
% 1.41/1.56  tff(150,plain,
% 1.41/1.56      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.56      inference(rewrite,[status(thm)],[])).
% 1.41/1.56  tff(151,plain,
% 1.41/1.56      (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) <=> ((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))) <=> ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 1.41/1.56      inference(bind,[status(th)],[])).
% 1.41/1.56  tff(152,plain,
% 1.41/1.56      (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.57      inference(quant_intro,[status(thm)],[151])).
% 1.41/1.57  tff(153,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_tsp_2')).
% 1.41/1.57  tff(154,plain,
% 1.41/1.57      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[153, 152])).
% 1.41/1.57  tff(155,plain,
% 1.41/1.57      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[154, 150])).
% 1.41/1.57  tff(156,plain,(
% 1.41/1.57      ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.57      inference(skolemize,[status(sab)],[155])).
% 1.41/1.57  tff(157,plain,
% 1.41/1.57      (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))) & m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[156, 149])).
% 1.41/1.57  tff(158,plain,
% 1.41/1.57      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[157, 147])).
% 1.41/1.57  tff(159,plain,
% 1.41/1.57      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[158, 145])).
% 1.41/1.57  tff(160,plain,
% 1.41/1.57      (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[159, 140])).
% 1.41/1.57  tff(161,plain,
% 1.41/1.57      (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))),
% 1.41/1.57      inference(rewrite,[status(thm)],[])).
% 1.41/1.57  tff(162,plain,
% 1.41/1.57      ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E)))))))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))),
% 1.41/1.57      inference(rewrite,[status(thm)],[])).
% 1.41/1.57  tff(163,plain,
% 1.41/1.57      (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))))),
% 1.41/1.57      inference(monotonicity,[status(thm)],[162])).
% 1.41/1.57  tff(164,plain,
% 1.41/1.57      (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))),
% 1.41/1.57      inference(transitivity,[status(thm)],[163, 161])).
% 1.41/1.57  tff(165,plain,
% 1.41/1.57      ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))),
% 1.41/1.57      inference(quant_inst,[status(thm)],[])).
% 1.41/1.57  tff(166,plain,
% 1.41/1.57      ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_3(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_3(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))),
% 1.41/1.57      inference(modus_ponens,[status(thm)],[165, 164])).
% 1.41/1.57  tff(167,plain,
% 1.41/1.57      (![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))),
% 1.41/1.57      inference(unit_resolution,[status(thm)],[166, 123, 122, 29, 160])).
% 1.41/1.57  tff(168,plain,
% 1.41/1.57      (v2_tsp_2(B!1, A!0)),
% 1.41/1.57      inference(and_elim,[status(thm)],[28])).
% 1.41/1.57  tff(169,plain,
% 1.41/1.57      (~v3_struct_0(B!1)),
% 1.41/1.57      inference(and_elim,[status(thm)],[28])).
% 1.41/1.57  tff(170,plain,
% 1.41/1.57      (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 1.41/1.57      inference(rewrite,[status(thm)],[])).
% 1.41/1.57  tff(171,plain,
% 1.41/1.57      ((v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))))) <=> (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 1.41/1.57      inference(rewrite,[status(thm)],[])).
% 1.41/1.57  tff(172,plain,
% 1.41/1.57      (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))))),
% 1.41/1.57      inference(monotonicity,[status(thm)],[171])).
% 1.41/1.57  tff(173,plain,
% 1.41/1.57      (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 1.41/1.57      inference(transitivity,[status(thm)],[172, 170])).
% 1.41/1.57  tff(174,plain,
% 1.41/1.57      ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))))))))),
% 1.41/1.58      inference(quant_inst,[status(thm)],[])).
% 1.41/1.58  tff(175,plain,
% 1.41/1.58      ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_3(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_3(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))),
% 1.41/1.58      inference(modus_ponens,[status(thm)],[174, 173])).
% 1.41/1.58  tff(176,plain,
% 1.41/1.58      (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[175, 169, 168, 36, 167])).
% 1.41/1.58  tff(177,plain,
% 1.41/1.58      (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 1.41/1.58      inference(bind,[status(th)],[])).
% 1.41/1.58  tff(178,plain,
% 1.41/1.58      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.58      inference(quant_intro,[status(thm)],[177])).
% 1.41/1.58  tff(179,plain,
% 1.41/1.58      (^[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)) | (~l1_pre_topc(A)) | (~v2_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_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)) | (~l1_pre_topc(A)) | (~v2_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_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)))))), (((~((~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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~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)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~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)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_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))) | (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)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 1.41/1.58      inference(bind,[status(th)],[])).
% 1.41/1.58  tff(180,plain,
% 1.41/1.58      (![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)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.58      inference(quant_intro,[status(thm)],[179])).
% 1.41/1.58  tff(181,plain,
% 1.41/1.58      (![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))))),
% 1.41/1.58      inference(rewrite,[status(thm)],[])).
% 1.41/1.58  tff(182,plain,
% 1.41/1.58      (^[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))))))),
% 1.41/1.58      inference(bind,[status(th)],[])).
% 1.41/1.58  tff(183,plain,
% 1.41/1.58      (![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))))),
% 1.41/1.58      inference(quant_intro,[status(thm)],[182])).
% 1.41/1.58  tff(184,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')).
% 1.41/1.58  tff(185,plain,
% 1.41/1.58      (![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))))),
% 1.41/1.58      inference(modus_ponens,[status(thm)],[184, 183])).
% 1.41/1.58  tff(186,plain,
% 1.41/1.58      (![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))))),
% 1.41/1.58      inference(modus_ponens,[status(thm)],[185, 181])).
% 1.41/1.58  tff(187,plain,(
% 1.41/1.58      ![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))))),
% 1.41/1.58      inference(skolemize,[status(sab)],[186])).
% 1.41/1.58  tff(188,plain,
% 1.41/1.58      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.58      inference(modus_ponens,[status(thm)],[187, 180])).
% 1.41/1.58  tff(189,plain,
% 1.41/1.58      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.58      inference(modus_ponens,[status(thm)],[188, 178])).
% 1.41/1.58  tff(190,plain,
% 1.41/1.58      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))))),
% 1.41/1.58      inference(rewrite,[status(thm)],[])).
% 1.41/1.58  tff(191,plain,
% 1.41/1.58      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))))),
% 1.41/1.58      inference(rewrite,[status(thm)],[])).
% 1.41/1.58  tff(192,plain,
% 1.41/1.58      ((~((~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))) | (~v1_funct_1(k1_tsp_2(A!0, B!1)))))),
% 1.41/1.58      inference(rewrite,[status(thm)],[])).
% 1.41/1.58  tff(193,plain,
% 1.41/1.58      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 1.41/1.58      inference(monotonicity,[status(thm)],[192])).
% 1.41/1.58  tff(194,plain,
% 1.41/1.58      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))))),
% 1.41/1.58      inference(transitivity,[status(thm)],[193, 191])).
% 1.41/1.58  tff(195,plain,
% 1.41/1.58      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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)))))))),
% 1.41/1.58      inference(monotonicity,[status(thm)],[194])).
% 1.41/1.58  tff(196,plain,
% 1.41/1.58      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))))),
% 1.41/1.58      inference(transitivity,[status(thm)],[195, 190])).
% 1.41/1.58  tff(197,plain,
% 1.41/1.58      ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~((~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))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 1.41/1.58      inference(quant_inst,[status(thm)],[])).
% 1.41/1.58  tff(198,plain,
% 1.41/1.58      ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~((~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))))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~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)))))),
% 1.41/1.58      inference(modus_ponens,[status(thm)],[197, 196])).
% 1.41/1.58  tff(199,plain,
% 1.41/1.58      ((~m1_pre_topc(B!1, A!0)) | (~((~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)))))),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[198, 123, 122, 29, 169, 168, 189])).
% 1.41/1.58  tff(200,plain,
% 1.41/1.58      (~((~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))))),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[199, 39])).
% 1.41/1.58  tff(201,plain,
% 1.41/1.58      (((~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_1(k1_tsp_2(A!0, B!1))),
% 1.41/1.58      inference(tautology,[status(thm)],[])).
% 1.41/1.58  tff(202,plain,
% 1.41/1.58      (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[201, 200])).
% 1.41/1.58  tff(203,plain,
% 1.41/1.58      (((~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)))) | m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.58      inference(tautology,[status(thm)],[])).
% 1.41/1.58  tff(204,plain,
% 1.41/1.58      (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[203, 200])).
% 1.41/1.58  tff(205,plain,
% 1.41/1.58      (((~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)))) | v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 1.41/1.58      inference(tautology,[status(thm)],[])).
% 1.41/1.58  tff(206,plain,
% 1.41/1.58      (v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[205, 200])).
% 1.41/1.58  tff(207,plain,
% 1.41/1.58      (((~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))),
% 1.41/1.58      inference(tautology,[status(thm)],[])).
% 1.41/1.58  tff(208,plain,
% 1.41/1.58      (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.58      inference(unit_resolution,[status(thm)],[207, 200])).
% 1.41/1.58  tff(209,plain,
% 1.41/1.58      (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | (~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 1.41/1.58      inference(rewrite,[status(thm)],[])).
% 1.41/1.58  tff(210,plain,
% 1.41/1.58      (((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 1.41/1.58      inference(rewrite,[status(thm)],[])).
% 1.41/1.58  tff(211,plain,
% 1.41/1.58      ((~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))) <=> (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))),
% 1.41/1.59      inference(rewrite,[status(thm)],[])).
% 1.41/1.59  tff(212,plain,
% 1.41/1.59      (((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))) <=> ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 1.41/1.59      inference(monotonicity,[status(thm)],[211])).
% 1.41/1.59  tff(213,plain,
% 1.41/1.59      (((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))) <=> ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 1.41/1.59      inference(transitivity,[status(thm)],[212, 210])).
% 1.41/1.59  tff(214,plain,
% 1.41/1.59      (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))))),
% 1.41/1.59      inference(monotonicity,[status(thm)],[213])).
% 1.41/1.59  tff(215,plain,
% 1.41/1.59      (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | (~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 1.41/1.59      inference(transitivity,[status(thm)],[214, 209])).
% 1.41/1.59  tff(216,plain,
% 1.41/1.59      ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))),
% 1.41/1.59      inference(quant_inst,[status(thm)],[])).
% 1.41/1.59  tff(217,plain,
% 1.41/1.59      ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_3(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | (~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))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))),
% 1.41/1.59      inference(modus_ponens,[status(thm)],[216, 215])).
% 1.41/1.59  tff(218,plain,
% 1.41/1.59      (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))),
% 1.41/1.59      inference(unit_resolution,[status(thm)],[217, 208, 206, 204, 202, 176])).
% 1.41/1.59  tff(219,plain,
% 1.41/1.59      (((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_3(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))),
% 1.41/1.59      inference(tautology,[status(thm)],[])).
% 1.41/1.59  tff(220,plain,
% 1.41/1.59      ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))),
% 1.41/1.59      inference(unit_resolution,[status(thm)],[219, 218])).
% 1.41/1.59  tff(221,plain,
% 1.41/1.59      (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 1.41/1.59      inference(bind,[status(th)],[])).
% 1.41/1.59  tff(222,plain,
% 1.41/1.59      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.59      inference(quant_intro,[status(thm)],[221])).
% 1.41/1.59  tff(223,plain,
% 1.41/1.59      (^[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)) | (~l1_pre_topc(A)) | (~v2_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_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)) | (~l1_pre_topc(A)) | (~v2_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))) | (k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 1.41/1.59      inference(bind,[status(th)],[])).
% 1.41/1.59  tff(224,plain,
% 1.41/1.59      (![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))) | (k4_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) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.59      inference(quant_intro,[status(thm)],[223])).
% 1.41/1.59  tff(225,plain,
% 1.41/1.59      (![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))) | (k4_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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 1.41/1.59      inference(rewrite,[status(thm)],[])).
% 1.41/1.59  tff(226,plain,
% 1.41/1.59      (^[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)) => (k4_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)) => (k4_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)) => (k4_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))) | (k4_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)) => (k4_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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))))),
% 1.41/1.59      inference(bind,[status(th)],[])).
% 1.41/1.59  tff(227,plain,
% 1.41/1.59      (![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)) => (k4_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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 1.41/1.59      inference(quant_intro,[status(thm)],[226])).
% 1.41/1.59  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)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_tsp_2')).
% 1.41/1.59  tff(229,plain,
% 1.41/1.59      (![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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 1.41/1.59      inference(modus_ponens,[status(thm)],[228, 227])).
% 1.41/1.59  tff(230,plain,
% 1.41/1.59      (![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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 1.41/1.59      inference(modus_ponens,[status(thm)],[229, 225])).
% 1.41/1.59  tff(231,plain,(
% 1.41/1.59      ![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))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 1.41/1.59      inference(skolemize,[status(sab)],[230])).
% 1.41/1.59  tff(232,plain,
% 1.41/1.59      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.59      inference(modus_ponens,[status(thm)],[231, 224])).
% 1.41/1.59  tff(233,plain,
% 1.41/1.59      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 1.41/1.59      inference(modus_ponens,[status(thm)],[232, 222])).
% 1.41/1.59  tff(234,plain,
% 1.41/1.59      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_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) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 1.41/1.59      inference(rewrite,[status(thm)],[])).
% 1.41/1.59  tff(235,plain,
% 1.41/1.59      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 1.41/1.59      inference(rewrite,[status(thm)],[])).
% 1.41/1.59  tff(236,plain,
% 1.41/1.59      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))))),
% 1.41/1.59      inference(monotonicity,[status(thm)],[235])).
% 1.41/1.59  tff(237,plain,
% 1.41/1.59      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 1.41/1.60      inference(transitivity,[status(thm)],[236, 234])).
% 1.41/1.60  tff(238,plain,
% 1.41/1.60      ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(239,plain,
% 1.41/1.60      ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[238, 237])).
% 1.41/1.60  tff(240,plain,
% 1.41/1.60      ((k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[239, 123, 122, 29, 169, 168, 233])).
% 1.41/1.60  tff(241,plain,
% 1.41/1.60      (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[240, 39])).
% 1.41/1.60  tff(242,plain,
% 1.41/1.60      (k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)),
% 1.41/1.60      inference(symmetry,[status(thm)],[241])).
% 1.41/1.60  tff(243,plain,
% 1.41/1.60      ((~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))),
% 1.41/1.60      inference(tautology,[status(thm)],[])).
% 1.41/1.60  tff(244,plain,
% 1.41/1.60      ((~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[243, 60, 242])).
% 1.41/1.60  tff(245,plain,
% 1.41/1.60      (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[244, 220])).
% 1.41/1.60  tff(246,plain,
% 1.41/1.60      (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2)))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2)))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(247,plain,
% 1.41/1.60      ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2)))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(248,plain,
% 1.41/1.60      ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[247, 246])).
% 1.41/1.60  tff(249,plain,
% 1.41/1.60      (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2)),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[248, 75, 245])).
% 1.41/1.60  tff(250,plain,
% 1.41/1.60      (k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, C!2))),
% 1.41/1.60      inference(symmetry,[status(thm)],[249])).
% 1.41/1.60  tff(251,plain,
% 1.41/1.60      (k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2) = k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2)),
% 1.41/1.60      inference(monotonicity,[status(thm)],[242])).
% 1.41/1.60  tff(252,plain,
% 1.41/1.60      (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), C!2)),
% 1.41/1.60      inference(symmetry,[status(thm)],[251])).
% 1.41/1.60  tff(253,plain,
% 1.41/1.60      (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1))),
% 1.41/1.60      inference(transitivity,[status(thm)],[252, 250, 138, 102, 82])).
% 1.41/1.60  tff(254,plain,
% 1.41/1.60      (^[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)))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(255,plain,
% 1.41/1.60      (![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))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[254])).
% 1.41/1.60  tff(256,plain,
% 1.41/1.60      (^[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)))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(257,plain,
% 1.41/1.60      (![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))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[256])).
% 1.41/1.60  tff(258,plain,
% 1.41/1.60      (![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))))),
% 1.41/1.60      inference(transitivity,[status(thm)],[257, 255])).
% 1.41/1.60  tff(259,plain,
% 1.41/1.60      (![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))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(260,plain,
% 1.41/1.60      (^[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))))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(261,plain,
% 1.41/1.60      (![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))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[260])).
% 1.41/1.60  tff(262,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')).
% 1.41/1.60  tff(263,plain,
% 1.41/1.60      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[262, 261])).
% 1.41/1.60  tff(264,plain,
% 1.41/1.60      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[263, 259])).
% 1.41/1.60  tff(265,plain,(
% 1.41/1.60      ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.41/1.60      inference(skolemize,[status(sab)],[264])).
% 1.41/1.60  tff(266,plain,
% 1.41/1.60      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[265, 258])).
% 1.41/1.60  tff(267,plain,
% 1.41/1.60      (((~![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))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(268,plain,
% 1.41/1.60      ((~![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))))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(269,plain,
% 1.41/1.60      ((~![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)))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[268, 267])).
% 1.41/1.60  tff(270,plain,
% 1.41/1.60      (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[269, 29, 266])).
% 1.41/1.60  tff(271,plain,
% 1.41/1.60      (((~![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)))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(272,plain,
% 1.41/1.60      ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(273,plain,
% 1.41/1.60      ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[272, 271])).
% 1.41/1.60  tff(274,plain,
% 1.41/1.60      (l1_pre_topc(B!1)),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[273, 36, 270])).
% 1.41/1.60  tff(275,plain,
% 1.41/1.60      (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(276,plain,
% 1.41/1.60      (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[275])).
% 1.41/1.60  tff(277,plain,
% 1.41/1.60      (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(278,plain,
% 1.41/1.60      (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(279,plain,
% 1.41/1.60      (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[278])).
% 1.41/1.60  tff(280,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 1.41/1.60  tff(281,plain,
% 1.41/1.60      (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[280, 279])).
% 1.41/1.60  tff(282,plain,
% 1.41/1.60      (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[281, 277])).
% 1.41/1.60  tff(283,plain,(
% 1.41/1.60      ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(skolemize,[status(sab)],[282])).
% 1.41/1.60  tff(284,plain,
% 1.41/1.60      (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[283, 276])).
% 1.41/1.60  tff(285,plain,
% 1.41/1.60      (((~![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)))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(286,plain,
% 1.41/1.60      ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(287,plain,
% 1.41/1.60      ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[286, 285])).
% 1.41/1.60  tff(288,plain,
% 1.41/1.60      (l1_struct_0(B!1)),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[287, 284, 274])).
% 1.41/1.60  tff(289,plain,
% 1.41/1.60      (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(290,plain,
% 1.41/1.60      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[289])).
% 1.41/1.60  tff(291,plain,
% 1.41/1.60      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(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)) | (~l1_pre_topc(A)) | (~v2_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(292,plain,
% 1.41/1.60      (![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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[291])).
% 1.41/1.60  tff(293,plain,
% 1.41/1.60      (![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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(294,plain,
% 1.41/1.60      (^[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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) <=> (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B))), ((((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(295,plain,
% 1.41/1.60      (![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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[294])).
% 1.41/1.60  tff(296,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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_tsp_2')).
% 1.41/1.60  tff(297,plain,
% 1.41/1.60      (![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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[296, 295])).
% 1.41/1.60  tff(298,plain,
% 1.41/1.60      (![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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[297, 293])).
% 1.41/1.60  tff(299,plain,(
% 1.41/1.60      ![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(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 1.41/1.60      inference(skolemize,[status(sab)],[298])).
% 1.41/1.60  tff(300,plain,
% 1.41/1.60      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[299, 292])).
% 1.41/1.60  tff(301,plain,
% 1.41/1.60      (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[300, 290])).
% 1.41/1.60  tff(302,plain,
% 1.41/1.60      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(303,plain,
% 1.41/1.60      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(304,plain,
% 1.41/1.60      ((~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(305,plain,
% 1.41/1.60      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.41/1.60      inference(monotonicity,[status(thm)],[304])).
% 1.41/1.60  tff(306,plain,
% 1.41/1.60      ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.41/1.60      inference(transitivity,[status(thm)],[305, 303])).
% 1.41/1.60  tff(307,plain,
% 1.41/1.60      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 1.41/1.60      inference(monotonicity,[status(thm)],[306])).
% 1.41/1.60  tff(308,plain,
% 1.41/1.60      (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.41/1.60      inference(transitivity,[status(thm)],[307, 302])).
% 1.41/1.60  tff(309,plain,
% 1.41/1.60      ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_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)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(310,plain,
% 1.41/1.60      ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[309, 308])).
% 1.41/1.60  tff(311,plain,
% 1.41/1.60      ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[310, 123, 122, 29, 169, 168, 301])).
% 1.41/1.60  tff(312,plain,
% 1.41/1.60      (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[311, 39])).
% 1.41/1.60  tff(313,plain,
% 1.41/1.60      (((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k4_tsp_2(A!0, B!1))),
% 1.41/1.60      inference(tautology,[status(thm)],[])).
% 1.41/1.60  tff(314,plain,
% 1.41/1.60      (v1_funct_1(k4_tsp_2(A!0, B!1))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[313, 312])).
% 1.41/1.60  tff(315,plain,
% 1.41/1.60      (((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.60      inference(tautology,[status(thm)],[])).
% 1.41/1.60  tff(316,plain,
% 1.41/1.60      (v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[315, 312])).
% 1.41/1.60  tff(317,plain,
% 1.41/1.60      (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.60      inference(monotonicity,[status(thm)],[242])).
% 1.41/1.60  tff(318,plain,
% 1.41/1.60      (^[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)))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(319,plain,
% 1.41/1.60      (![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))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[318])).
% 1.41/1.60  tff(320,plain,
% 1.41/1.60      (![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))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(321,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')).
% 1.41/1.60  tff(322,plain,
% 1.41/1.60      (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[321, 320])).
% 1.41/1.60  tff(323,plain,(
% 1.41/1.60      ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.41/1.60      inference(skolemize,[status(sab)],[322])).
% 1.41/1.60  tff(324,plain,
% 1.41/1.60      (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[323, 319])).
% 1.41/1.60  tff(325,plain,
% 1.41/1.60      ((~![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)))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(326,plain,
% 1.41/1.60      (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))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[325, 324])).
% 1.41/1.60  tff(327,plain,
% 1.41/1.60      ((~(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))),
% 1.41/1.60      inference(tautology,[status(thm)],[])).
% 1.41/1.60  tff(328,plain,
% 1.41/1.60      ((~(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))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[327, 204])).
% 1.41/1.60  tff(329,plain,
% 1.41/1.60      (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[328, 326])).
% 1.41/1.60  tff(330,plain,
% 1.41/1.60      (m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[329, 317])).
% 1.41/1.60  tff(331,plain,
% 1.41/1.60      (((~![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)))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(332,plain,
% 1.41/1.60      ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 1.41/1.60      inference(quant_inst,[status(thm)],[])).
% 1.41/1.60  tff(333,plain,
% 1.41/1.60      ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 1.41/1.60      inference(modus_ponens,[status(thm)],[332, 331])).
% 1.41/1.60  tff(334,plain,
% 1.41/1.60      (l1_struct_0(A!0)),
% 1.41/1.60      inference(unit_resolution,[status(thm)],[333, 29, 284])).
% 1.41/1.60  tff(335,plain,
% 1.41/1.60      (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) <=> (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(336,plain,
% 1.41/1.60      (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[335])).
% 1.41/1.60  tff(337,plain,
% 1.41/1.60      (^[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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))))),
% 1.41/1.60      inference(bind,[status(th)],[])).
% 1.41/1.60  tff(338,plain,
% 1.41/1.60      (![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))),
% 1.41/1.60      inference(quant_intro,[status(thm)],[337])).
% 1.41/1.60  tff(339,plain,
% 1.41/1.60      (![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 1.41/1.60      inference(rewrite,[status(thm)],[])).
% 1.41/1.60  tff(340,plain,
% 1.41/1.60      (^[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))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(341,plain,
% 1.41/1.61      (![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))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[340])).
% 1.41/1.61  tff(342,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))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_pre_topc')).
% 1.41/1.61  tff(343,plain,
% 1.41/1.61      (![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[342, 341])).
% 1.41/1.61  tff(344,plain,
% 1.41/1.61      (![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[343, 339])).
% 1.41/1.61  tff(345,plain,(
% 1.41/1.61      ![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)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 1.41/1.61      inference(skolemize,[status(sab)],[344])).
% 1.41/1.61  tff(346,plain,
% 1.41/1.61      (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[345, 338])).
% 1.41/1.61  tff(347,plain,
% 1.41/1.61      (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[346, 336])).
% 1.41/1.61  tff(348,plain,
% 1.41/1.61      (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 1.41/1.61      inference(rewrite,[status(thm)],[])).
% 1.41/1.61  tff(349,plain,
% 1.41/1.61      ((m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_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(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 1.41/1.61      inference(rewrite,[status(thm)],[])).
% 1.41/1.61  tff(350,plain,
% 1.41/1.61      (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.41/1.61      inference(monotonicity,[status(thm)],[349])).
% 1.41/1.61  tff(351,plain,
% 1.41/1.61      (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 1.41/1.61      inference(transitivity,[status(thm)],[350, 348])).
% 1.41/1.61  tff(352,plain,
% 1.41/1.61      ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 1.41/1.61      inference(quant_inst,[status(thm)],[])).
% 1.41/1.61  tff(353,plain,
% 1.41/1.61      ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(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!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[352, 351])).
% 1.41/1.61  tff(354,plain,
% 1.41/1.61      ((~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 1.41/1.61      inference(unit_resolution,[status(thm)],[353, 347, 334])).
% 1.41/1.61  tff(355,plain,
% 1.41/1.61      (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))),
% 1.41/1.61      inference(unit_resolution,[status(thm)],[354, 330, 316, 314, 288])).
% 1.41/1.61  tff(356,plain,
% 1.41/1.61      (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(357,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[356])).
% 1.41/1.61  tff(358,plain,
% 1.41/1.61      (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(359,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[358])).
% 1.41/1.61  tff(360,plain,
% 1.41/1.61      (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(361,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[360])).
% 1.41/1.61  tff(362,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.41/1.61      inference(transitivity,[status(thm)],[361, 359])).
% 1.41/1.61  tff(363,plain,
% 1.41/1.61      (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(364,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[363])).
% 1.41/1.61  tff(365,plain,
% 1.41/1.61      (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | ((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & ((v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(366,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | ((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & ((v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[365])).
% 1.41/1.61  tff(367,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.41/1.61      inference(rewrite,[status(thm)],[])).
% 1.41/1.61  tff(368,plain,
% 1.41/1.61      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))) <=> (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))), ((l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> (l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), rewrite((l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))), ((l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))))), (![B: $i] : (l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), ((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), ((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))))),
% 1.41/1.61      inference(bind,[status(th)],[])).
% 1.41/1.61  tff(369,plain,
% 1.41/1.61      (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.41/1.61      inference(quant_intro,[status(thm)],[368])).
% 1.41/1.61  tff(370,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => (v3_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tsp_1')).
% 1.41/1.61  tff(371,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[370, 369])).
% 1.41/1.61  tff(372,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m1_tsp_1(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (v3_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[371, 367])).
% 1.41/1.61  tff(373,plain,(
% 1.41/1.61      ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | ((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & ((v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))),
% 1.41/1.61      inference(skolemize,[status(sab)],[372])).
% 1.41/1.61  tff(374,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m1_tsp_1(B, A)) | (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (((~v3_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_4(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B))))) & (v3_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v3_pre_topc(tptp_fun_C_5(B, A), B) | (m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(tptp_fun_D_6(B, A), A) & (tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B))))) & ((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D, A) & (tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[373, 366])).
% 1.41/1.61  tff(375,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[374, 364])).
% 1.41/1.61  tff(376,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[375, 362])).
% 1.41/1.61  tff(377,plain,
% 1.41/1.61      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.41/1.61      inference(modus_ponens,[status(thm)],[376, 357])).
% 1.41/1.61  tff(378,plain,
% 1.41/1.61      (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.41/1.62      inference(rewrite,[status(thm)],[])).
% 1.41/1.62  tff(379,plain,
% 1.41/1.62      (((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(D, A!0)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) <=> ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.41/1.62      inference(rewrite,[status(thm)],[])).
% 1.41/1.62  tff(380,plain,
% 1.41/1.62      (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(D, A!0)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))))),
% 1.41/1.62      inference(monotonicity,[status(thm)],[379])).
% 1.41/1.62  tff(381,plain,
% 1.41/1.62      (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(D, A!0)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.41/1.62      inference(transitivity,[status(thm)],[380, 378])).
% 1.41/1.62  tff(382,plain,
% 1.41/1.62      ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(D, A!0)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.41/1.62      inference(quant_inst,[status(thm)],[])).
% 1.41/1.62  tff(383,plain,
% 1.41/1.62      ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A), B) | (~((~m1_subset_1(tptp_fun_D_6(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_6(B, A), A)) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(tptp_fun_D_6(B, A), u1_struct_0(B)))))))) | (~((~v3_pre_topc(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~v3_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_5(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m1_tsp_1(B, A)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B, A), u1_struct_0(B)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))),
% 1.41/1.62      inference(modus_ponens,[status(thm)],[382, 381])).
% 1.41/1.62  tff(384,plain,
% 1.41/1.62      (![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))),
% 1.41/1.62      inference(unit_resolution,[status(thm)],[383, 29, 377])).
% 1.41/1.62  tff(385,plain,
% 1.41/1.62      (((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | ((~l1_pre_topc(B!1)) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | (~l1_pre_topc(B!1)) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))),
% 1.41/1.62      inference(rewrite,[status(thm)],[])).
% 1.41/1.62  tff(386,plain,
% 1.41/1.62      (((~l1_pre_topc(B!1)) | (~((~(m1_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))))))))) <=> ((~l1_pre_topc(B!1)) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))),
% 1.41/1.62      inference(rewrite,[status(thm)],[])).
% 1.41/1.62  tff(387,plain,
% 1.41/1.62      (((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | ((~l1_pre_topc(B!1)) | (~((~(m1_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | ((~l1_pre_topc(B!1)) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))))))))))),
% 1.41/1.62      inference(monotonicity,[status(thm)],[386])).
% 1.41/1.62  tff(388,plain,
% 1.41/1.62      (((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | ((~l1_pre_topc(B!1)) | (~((~(m1_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))) <=> ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | (~l1_pre_topc(B!1)) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))),
% 1.41/1.63      inference(transitivity,[status(thm)],[387, 385])).
% 1.41/1.63  tff(389,plain,
% 1.41/1.63      ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | ((~l1_pre_topc(B!1)) | (~((~(m1_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))))),
% 1.41/1.63      inference(quant_inst,[status(thm)],[])).
% 1.41/1.63  tff(390,plain,
% 1.41/1.63      ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m1_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v3_pre_topc(tptp_fun_C_5(B, A!0), B)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v3_pre_topc(tptp_fun_C_5(B, A!0), B) | (~((~(tptp_fun_C_5(B, A!0) = k3_xboole_0(tptp_fun_D_6(B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_6(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_6(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) | (~((~m1_tsp_1(B, A!0)) | (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | (~((~((~v3_pre_topc(C, B)) | (~((~(C = k3_xboole_0(tptp_fun_D_4(C, B, A!0), u1_struct_0(B)))) | (~v3_pre_topc(tptp_fun_D_4(C, B, A!0), A!0)) | (~m1_subset_1(tptp_fun_D_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~(v3_pre_topc(C, B) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))) | (~l1_pre_topc(B!1)) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))))))))),
% 1.41/1.63      inference(modus_ponens,[status(thm)],[389, 388])).
% 1.41/1.63  tff(391,plain,
% 1.41/1.63      (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))))),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[390, 274, 384])).
% 1.41/1.63  tff(392,plain,
% 1.41/1.63      (((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | m1_tsp_1(B!1, A!0) | (~((~m1_subset_1(tptp_fun_C_5(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1)) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~(v3_pre_topc(tptp_fun_C_5(B!1, A!0), B!1) | (~((~m1_subset_1(tptp_fun_D_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_6(B!1, A!0), A!0)) | (~(tptp_fun_C_5(B!1, A!0) = k3_xboole_0(tptp_fun_D_6(B!1, A!0), u1_struct_0(B!1)))))))))))) | (~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))))))) | ((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))),
% 1.41/1.63      inference(tautology,[status(thm)],[])).
% 1.41/1.63  tff(393,plain,
% 1.41/1.63      ((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))))),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[392, 391])).
% 1.41/1.63  tff(394,plain,
% 1.41/1.63      (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 1.41/1.63      inference(bind,[status(th)],[])).
% 1.41/1.63  tff(395,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(quant_intro,[status(thm)],[394])).
% 1.41/1.63  tff(396,plain,
% 1.41/1.63      (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 1.41/1.63      inference(bind,[status(th)],[])).
% 1.41/1.63  tff(397,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(quant_intro,[status(thm)],[396])).
% 1.41/1.63  tff(398,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(transitivity,[status(thm)],[397, 395])).
% 1.41/1.63  tff(399,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(rewrite,[status(thm)],[])).
% 1.41/1.63  tff(400,plain,
% 1.41/1.63      (^[A: $i] : rewrite((l1_pre_topc(A) => ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 1.41/1.63      inference(bind,[status(th)],[])).
% 1.41/1.63  tff(401,plain,
% 1.41/1.63      (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(quant_intro,[status(thm)],[400])).
% 1.41/1.63  tff(402,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m1_tsp_1')).
% 1.41/1.63  tff(403,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(modus_ponens,[status(thm)],[402, 401])).
% 1.41/1.63  tff(404,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(modus_ponens,[status(thm)],[403, 399])).
% 1.41/1.63  tff(405,plain,(
% 1.41/1.63      ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(skolemize,[status(sab)],[404])).
% 1.41/1.63  tff(406,plain,
% 1.41/1.63      (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 1.41/1.63      inference(modus_ponens,[status(thm)],[405, 398])).
% 1.41/1.63  tff(407,plain,
% 1.41/1.63      (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m1_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m1_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 1.41/1.63      inference(rewrite,[status(thm)],[])).
% 1.41/1.63  tff(408,plain,
% 1.41/1.63      ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m1_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 1.41/1.63      inference(quant_inst,[status(thm)],[])).
% 1.41/1.63  tff(409,plain,
% 1.41/1.63      ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m1_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m1_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 1.41/1.63      inference(modus_ponens,[status(thm)],[408, 407])).
% 1.41/1.63  tff(410,plain,
% 1.41/1.63      (![B: $i] : (m1_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[409, 29, 406])).
% 1.41/1.63  tff(411,plain,
% 1.41/1.63      ((~![B: $i] : (m1_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))) | (m1_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))),
% 1.41/1.63      inference(quant_inst,[status(thm)],[])).
% 1.41/1.63  tff(412,plain,
% 1.41/1.63      (m1_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[411, 410])).
% 1.41/1.63  tff(413,plain,
% 1.41/1.63      ((~(m1_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_tsp_1(B!1, A!0) | (~m1_pre_topc(B!1, A!0))),
% 1.41/1.63      inference(tautology,[status(thm)],[])).
% 1.41/1.63  tff(414,plain,
% 1.41/1.63      ((~(m1_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_tsp_1(B!1, A!0)),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[413, 39])).
% 1.41/1.63  tff(415,plain,
% 1.41/1.63      (m1_tsp_1(B!1, A!0)),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[414, 412])).
% 1.41/1.63  tff(416,plain,
% 1.41/1.63      ((~((~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))))) | (~m1_tsp_1(B!1, A!0)) | (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))))),
% 1.41/1.63      inference(tautology,[status(thm)],[])).
% 1.41/1.63  tff(417,plain,
% 1.41/1.63      (~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))))),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[416, 415, 393])).
% 1.41/1.63  tff(418,plain,
% 1.41/1.63      (((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1)))))))))))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))),
% 1.41/1.63      inference(tautology,[status(thm)],[])).
% 1.41/1.63  tff(419,plain,
% 1.41/1.63      (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))),
% 1.41/1.63      inference(unit_resolution,[status(thm)],[418, 417])).
% 1.41/1.63  tff(420,plain,
% 1.41/1.63      (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))))))),
% 1.41/1.63      inference(rewrite,[status(thm)],[])).
% 1.41/1.63  tff(421,plain,
% 1.41/1.63      (((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))))))) <=> ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))))))),
% 1.41/1.63      inference(rewrite,[status(thm)],[])).
% 1.41/1.63  tff(422,plain,
% 1.41/1.63      (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1))))))))))))),
% 1.49/1.64      inference(monotonicity,[status(thm)],[421])).
% 1.49/1.64  tff(423,plain,
% 1.49/1.64      (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))))))),
% 1.49/1.64      inference(transitivity,[status(thm)],[422, 420])).
% 1.49/1.64  tff(424,plain,
% 1.49/1.64      ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))))))),
% 1.49/1.64      inference(quant_inst,[status(thm)],[])).
% 1.49/1.64  tff(425,plain,
% 1.49/1.64      ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v3_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v3_pre_topc(C, B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1))))))))))),
% 1.49/1.64      inference(modus_ponens,[status(thm)],[424, 423])).
% 1.49/1.64  tff(426,plain,
% 1.49/1.64      ((~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1))))))))))),
% 1.49/1.64      inference(unit_resolution,[status(thm)],[425, 419])).
% 1.49/1.64  tff(427,plain,
% 1.49/1.64      (~((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1)))))))))),
% 1.49/1.64      inference(unit_resolution,[status(thm)],[426, 355])).
% 1.49/1.64  tff(428,plain,
% 1.49/1.64      (((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | (~((~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), A!0)) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(tptp_fun_D_4(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1, A!0), u1_struct_0(B!1))))))))) | (v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))),
% 1.49/1.65      inference(tautology,[status(thm)],[])).
% 1.49/1.65  tff(429,plain,
% 1.49/1.65      (v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))),
% 1.49/1.65      inference(unit_resolution,[status(thm)],[428, 427])).
% 1.49/1.65  tff(430,plain,
% 1.49/1.65      (~v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)),
% 1.49/1.65      inference(or_elim,[status(thm)],[74])).
% 1.49/1.65  tff(431,plain,
% 1.49/1.65      ((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))),
% 1.49/1.65      inference(tautology,[status(thm)],[])).
% 1.49/1.65  tff(432,plain,
% 1.49/1.65      ((~(v3_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1))))))) | ![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))),
% 1.49/1.65      inference(unit_resolution,[status(thm)],[431, 430])).
% 1.49/1.65  tff(433,plain,
% 1.49/1.65      (![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))),
% 1.49/1.65      inference(unit_resolution,[status(thm)],[432, 429])).
% 1.49/1.65  tff(434,plain,
% 1.49/1.65      (((~![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))) | ((~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1)))))) <=> ((~![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1)))))),
% 1.49/1.65      inference(rewrite,[status(thm)],[])).
% 1.49/1.65  tff(435,plain,
% 1.49/1.65      ((~![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))) | ((~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1)))))),
% 1.49/1.65      inference(quant_inst,[status(thm)],[])).
% 1.49/1.65  tff(436,plain,
% 1.49/1.65      ((~![D: $i] : ((~v3_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))) | (~v3_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1))))),
% 1.49/1.65      inference(modus_ponens,[status(thm)],[435, 434])).
% 1.49/1.65  tff(437,plain,
% 1.49/1.65      (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1)))),
% 1.49/1.65      inference(unit_resolution,[status(thm)],[436, 131, 75, 433])).
% 1.49/1.65  tff(438,plain,
% 1.49/1.65      ($false),
% 1.49/1.65      inference(unit_resolution,[status(thm)],[437, 253])).
% 1.49/1.65  % SZS output end Proof
% 1.49/1.65  % E exiting
%------------------------------------------------------------------------------