TSTP Solution File: TOP042+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP042+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 30 01:56:02 EDT 2022
% Result : Theorem 0.84s 0.86s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP042+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 11:12:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.84/0.86 % SZS status Theorem
% 0.84/0.86 % SZS output start Proof
% 0.84/0.86 tff(k3_xboole_0_type, type, (
% 0.84/0.86 k3_xboole_0: ( $i * $i ) > $i)).
% 0.84/0.86 tff(u1_struct_0_type, type, (
% 0.84/0.86 u1_struct_0: $i > $i)).
% 0.84/0.86 tff(tptp_fun_B_1_type, type, (
% 0.84/0.86 tptp_fun_B_1: $i)).
% 0.84/0.86 tff(tptp_fun_C_2_type, type, (
% 0.84/0.86 tptp_fun_C_2: $i)).
% 0.84/0.86 tff(k4_pre_topc_type, type, (
% 0.84/0.86 k4_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 0.84/0.86 tff(k4_tsp_2_type, type, (
% 0.84/0.86 k4_tsp_2: ( $i * $i ) > $i)).
% 0.84/0.86 tff(tptp_fun_A_0_type, type, (
% 0.84/0.86 tptp_fun_A_0: $i)).
% 0.84/0.86 tff(k5_subset_1_type, type, (
% 0.84/0.86 k5_subset_1: ( $i * $i * $i ) > $i)).
% 0.84/0.86 tff(m1_subset_1_type, type, (
% 0.84/0.86 m1_subset_1: ( $i * $i ) > $o)).
% 0.84/0.86 tff(k1_zfmisc_1_type, type, (
% 0.84/0.86 k1_zfmisc_1: $i > $i)).
% 0.84/0.86 tff(m1_pre_topc_type, type, (
% 0.84/0.86 m1_pre_topc: ( $i * $i ) > $o)).
% 0.84/0.86 tff(m2_tsp_1_type, type, (
% 0.84/0.86 m2_tsp_1: ( $i * $i ) > $o)).
% 0.84/0.86 tff(l1_pre_topc_type, type, (
% 0.84/0.86 l1_pre_topc: $i > $o)).
% 0.84/0.86 tff(v4_pre_topc_type, type, (
% 0.84/0.86 v4_pre_topc: ( $i * $i ) > $o)).
% 0.84/0.86 tff(v2_tsp_2_type, type, (
% 0.84/0.86 v2_tsp_2: ( $i * $i ) > $o)).
% 0.84/0.86 tff(v3_struct_0_type, type, (
% 0.84/0.86 v3_struct_0: $i > $o)).
% 0.84/0.86 tff(v2_pre_topc_type, type, (
% 0.84/0.86 v2_pre_topc: $i > $o)).
% 0.84/0.86 tff(k3_tex_4_type, type, (
% 0.84/0.86 k3_tex_4: ( $i * $i ) > $i)).
% 0.84/0.86 tff(k1_tsp_2_type, type, (
% 0.84/0.86 k1_tsp_2: ( $i * $i ) > $i)).
% 0.84/0.86 tff(tptp_fun_E_4_type, type, (
% 0.84/0.86 tptp_fun_E_4: ( $i * $i * $i ) > $i)).
% 0.84/0.86 tff(tptp_fun_D_3_type, type, (
% 0.84/0.86 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.84/0.86 tff(m2_relset_1_type, type, (
% 0.84/0.86 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.84/0.86 tff(v5_pre_topc_type, type, (
% 0.84/0.86 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 0.84/0.86 tff(v1_funct_2_type, type, (
% 0.84/0.86 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.84/0.86 tff(v1_funct_1_type, type, (
% 0.84/0.86 v1_funct_1: $i > $o)).
% 0.84/0.86 tff(tptp_fun_D_5_type, type, (
% 0.84/0.86 tptp_fun_D_5: ( $i * $i * $i ) > $i)).
% 0.84/0.86 tff(l1_struct_0_type, type, (
% 0.84/0.86 l1_struct_0: $i > $o)).
% 0.84/0.86 tff(m1_relset_1_type, type, (
% 0.84/0.86 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.84/0.86 tff(r1_tarski_type, type, (
% 0.84/0.86 r1_tarski: ( $i * $i ) > $o)).
% 0.84/0.86 tff(tptp_fun_C_6_type, type, (
% 0.84/0.86 tptp_fun_C_6: ( $i * $i ) > $i)).
% 0.84/0.86 tff(tptp_fun_D_7_type, type, (
% 0.84/0.86 tptp_fun_D_7: ( $i * $i ) > $i)).
% 0.84/0.86 tff(1,plain,
% 0.84/0.86 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 0.84/0.86 inference(bind,[status(th)],[])).
% 0.84/0.86 tff(2,plain,
% 0.84/0.86 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.84/0.86 inference(quant_intro,[status(thm)],[1])).
% 0.84/0.86 tff(3,plain,
% 0.84/0.86 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(4,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.84/0.86 tff(5,plain,
% 0.84/0.86 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.84/0.86 tff(6,plain,(
% 0.84/0.86 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.84/0.86 inference(skolemize,[status(sab)],[5])).
% 0.84/0.86 tff(7,plain,
% 0.84/0.86 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.84/0.86 tff(8,plain,
% 0.84/0.86 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(C!2, u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(B!1), C!2))),
% 0.84/0.86 inference(quant_inst,[status(thm)],[])).
% 0.84/0.86 tff(9,plain,
% 0.84/0.86 (k3_xboole_0(C!2, u1_struct_0(B!1)) = k3_xboole_0(u1_struct_0(B!1), C!2)),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.84/0.86 tff(10,plain,
% 0.84/0.86 (k3_xboole_0(u1_struct_0(B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1))),
% 0.84/0.86 inference(symmetry,[status(thm)],[9])).
% 0.84/0.86 tff(11,plain,
% 0.84/0.86 (^[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))))),
% 0.84/0.86 inference(bind,[status(th)],[])).
% 0.84/0.86 tff(12,plain,
% 0.84/0.86 (![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)))),
% 0.84/0.86 inference(quant_intro,[status(thm)],[11])).
% 0.84/0.86 tff(13,plain,
% 0.84/0.86 (^[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))))),
% 0.84/0.86 inference(bind,[status(th)],[])).
% 0.84/0.86 tff(14,plain,
% 0.84/0.86 (![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)))),
% 0.84/0.86 inference(quant_intro,[status(thm)],[13])).
% 0.84/0.86 tff(15,plain,
% 0.84/0.86 (![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)))),
% 0.84/0.86 inference(transitivity,[status(thm)],[14, 12])).
% 0.84/0.86 tff(16,plain,
% 0.84/0.86 (![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)))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(17,plain,
% 0.84/0.86 (^[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))))),
% 0.84/0.86 inference(bind,[status(th)],[])).
% 0.84/0.86 tff(18,plain,
% 0.84/0.86 (![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)))),
% 0.84/0.86 inference(quant_intro,[status(thm)],[17])).
% 0.84/0.86 tff(19,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_tsp_1')).
% 0.84/0.86 tff(20,plain,
% 0.84/0.86 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.84/0.86 tff(21,plain,
% 0.84/0.86 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.84/0.86 tff(22,plain,(
% 0.84/0.86 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.84/0.86 inference(skolemize,[status(sab)],[21])).
% 0.84/0.86 tff(23,plain,
% 0.84/0.86 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.84/0.86 tff(24,plain,
% 0.84/0.86 ((((~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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(25,plain,
% 0.84/0.86 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(26,plain,
% 0.84/0.86 ((~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(27,plain,
% 0.84/0.86 ((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(28,plain,
% 0.84/0.86 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_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)) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.84/0.86 inference(monotonicity,[status(thm)],[27, 26])).
% 0.84/0.86 tff(29,plain,
% 0.84/0.86 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.84/0.86 inference(transitivity,[status(thm)],[28, 25])).
% 0.84/0.86 tff(30,plain,
% 0.84/0.86 ((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(31,plain,
% 0.84/0.86 (((~(~((~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)))) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 1.00/0.86 inference(monotonicity,[status(thm)],[30, 29])).
% 1.00/0.86 tff(32,plain,
% 1.00/0.86 (((~(~((~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)))) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 1.00/0.86 inference(transitivity,[status(thm)],[31, 24])).
% 1.00/0.86 tff(33,plain,
% 1.00/0.86 ((~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(34,plain,
% 1.00/0.86 ((~![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))) => (v4_pre_topc(C, A) => v4_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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(35,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))) => (v4_pre_topc(C, A) => v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t35_tsp_2')).
% 1.00/0.86 tff(36,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.00/0.86 tff(37,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[36, 33])).
% 1.00/0.86 tff(38,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.00/0.86 tff(39,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[38, 33])).
% 1.00/0.86 tff(40,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[39, 33])).
% 1.00/0.86 tff(41,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.00/0.86 tff(42,plain,
% 1.00/0.86 (~![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] : (v4_pre_topc(k4_pre_topc(A, B, k4_tsp_2(A, B), C), B) | (~v4_pre_topc(C, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[41, 33])).
% 1.00/0.86 tff(43,plain,
% 1.00/0.86 ((~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) & (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[42, 32])).
% 1.00/0.86 tff(44,plain,
% 1.00/0.86 (l1_pre_topc(A!0)),
% 1.00/0.86 inference(and_elim,[status(thm)],[43])).
% 1.00/0.86 tff(45,plain,
% 1.00/0.86 (((~![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)))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(46,plain,
% 1.00/0.86 ((~![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)))),
% 1.00/0.86 inference(quant_inst,[status(thm)],[])).
% 1.00/0.86 tff(47,plain,
% 1.00/0.86 ((~![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))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.00/0.86 tff(48,plain,
% 1.00/0.86 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[47, 44, 23])).
% 1.00/0.86 tff(49,plain,
% 1.00/0.86 ((~![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))),
% 1.00/0.86 inference(quant_inst,[status(thm)],[])).
% 1.00/0.86 tff(50,plain,
% 1.00/0.86 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.00/0.86 tff(51,plain,
% 1.00/0.86 (m2_tsp_1(B!1, A!0)),
% 1.00/0.86 inference(and_elim,[status(thm)],[43])).
% 1.00/0.86 tff(52,plain,
% 1.00/0.86 ((~(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)),
% 1.00/0.86 inference(tautology,[status(thm)],[])).
% 1.00/0.86 tff(53,plain,
% 1.00/0.86 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.00/0.86 tff(54,plain,
% 1.00/0.86 (m1_pre_topc(B!1, A!0)),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[53, 50])).
% 1.00/0.86 tff(55,plain,
% 1.00/0.86 (^[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))))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(56,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[55])).
% 1.00/0.86 tff(57,plain,
% 1.00/0.86 (^[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))))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(58,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[57])).
% 1.00/0.86 tff(59,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(transitivity,[status(thm)],[58, 56])).
% 1.00/0.86 tff(60,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(61,plain,
% 1.00/0.86 (^[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)))))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(62,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[61])).
% 1.00/0.86 tff(63,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_tsep_1')).
% 1.00/0.86 tff(64,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.00/0.86 tff(65,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.00/0.86 tff(66,plain,(
% 1.00/0.86 ![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)))))),
% 1.00/0.86 inference(skolemize,[status(sab)],[65])).
% 1.00/0.86 tff(67,plain,
% 1.00/0.86 (![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)))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.00/0.86 tff(68,plain,
% 1.00/0.86 (((~![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)))))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(69,plain,
% 1.00/0.86 ((~![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)))))),
% 1.00/0.86 inference(quant_inst,[status(thm)],[])).
% 1.00/0.86 tff(70,plain,
% 1.00/0.86 ((~![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))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.00/0.86 tff(71,plain,
% 1.00/0.86 (![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[70, 44, 67])).
% 1.00/0.86 tff(72,plain,
% 1.00/0.86 (((~![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))))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(73,plain,
% 1.00/0.86 ((~![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))))),
% 1.00/0.86 inference(quant_inst,[status(thm)],[])).
% 1.00/0.86 tff(74,plain,
% 1.00/0.86 ((~![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)))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.00/0.86 tff(75,plain,
% 1.00/0.86 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[74, 71, 54])).
% 1.00/0.86 tff(76,plain,
% 1.00/0.86 (^[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)))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(77,plain,
% 1.00/0.86 (![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))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[76])).
% 1.00/0.86 tff(78,plain,
% 1.00/0.86 (^[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))))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(79,plain,
% 1.00/0.86 (![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))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[78])).
% 1.00/0.86 tff(80,plain,
% 1.00/0.86 (![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)))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(81,plain,
% 1.00/0.86 (^[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))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(82,plain,
% 1.00/0.86 (![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)))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[81])).
% 1.00/0.86 tff(83,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/sandbox/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 1.00/0.86 tff(84,plain,
% 1.00/0.86 (![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)))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.00/0.86 tff(85,plain,
% 1.00/0.86 (![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)))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[84, 80])).
% 1.00/0.86 tff(86,plain,(
% 1.00/0.86 ![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)))),
% 1.00/0.86 inference(skolemize,[status(sab)],[85])).
% 1.00/0.86 tff(87,plain,
% 1.00/0.86 (![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))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[86, 79])).
% 1.00/0.86 tff(88,plain,
% 1.00/0.86 (![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))))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[87, 77])).
% 1.00/0.86 tff(89,plain,
% 1.00/0.86 (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.00/0.86 inference(and_elim,[status(thm)],[43])).
% 1.00/0.86 tff(90,plain,
% 1.00/0.86 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.00/0.86 inference(or_elim,[status(thm)],[89])).
% 1.00/0.86 tff(91,plain,
% 1.00/0.86 (((~![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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)))) <=> ((~![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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(92,plain,
% 1.00/0.86 (((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)) | (~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) = k3_xboole_0(u1_struct_0(B!1), C!2)))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(93,plain,
% 1.00/0.86 (((~![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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)) | (~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) = 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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2))))),
% 1.00/0.86 inference(monotonicity,[status(thm)],[92])).
% 1.00/0.86 tff(94,plain,
% 1.00/0.86 (((~![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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)) | (~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) = 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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)))),
% 1.00/0.86 inference(transitivity,[status(thm)],[93, 91])).
% 1.00/0.86 tff(95,plain,
% 1.00/0.86 ((~![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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)) | (~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)))))),
% 1.00/0.86 inference(quant_inst,[status(thm)],[])).
% 1.00/0.86 tff(96,plain,
% 1.00/0.86 ((~![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), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2))),
% 1.00/0.86 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.00/0.86 tff(97,plain,
% 1.00/0.86 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), C!2)),
% 1.00/0.86 inference(unit_resolution,[status(thm)],[96, 90, 88, 75])).
% 1.00/0.86 tff(98,plain,
% 1.00/0.86 (^[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)))) | (~v4_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)))) | (~v4_pre_topc(B, A)))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(99,plain,
% 1.00/0.86 (![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[98])).
% 1.00/0.86 tff(100,plain,
% 1.00/0.86 (^[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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(101,plain,
% 1.00/0.86 (![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[100])).
% 1.00/0.86 tff(102,plain,
% 1.00/0.86 (^[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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(103,plain,
% 1.00/0.86 (![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[102])).
% 1.00/0.86 tff(104,plain,
% 1.00/0.86 (![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.00/0.86 inference(transitivity,[status(thm)],[103, 101])).
% 1.00/0.86 tff(105,plain,
% 1.00/0.86 (^[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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(106,plain,
% 1.00/0.86 (![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[105])).
% 1.00/0.86 tff(107,plain,
% 1.00/0.86 (![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.86 inference(rewrite,[status(thm)],[])).
% 1.00/0.86 tff(108,plain,
% 1.00/0.86 (^[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((v4_pre_topc(B, A) => (k3_tex_4(A, B) = B)) <=> ((~v4_pre_topc(B, A)) | (k3_tex_4(A, B) = B))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v4_pre_topc(B, A)) | (k3_tex_4(A, B) = B))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v4_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)))) | (~v4_pre_topc(B, A)))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_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)))) | (~v4_pre_topc(B, A)))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_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)))) | (~v4_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))) => (v4_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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_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))) => (v4_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)))) | (~v4_pre_topc(B, A))))))),
% 1.00/0.86 inference(bind,[status(th)],[])).
% 1.00/0.86 tff(109,plain,
% 1.00/0.86 (![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))) => (v4_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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.86 inference(quant_intro,[status(thm)],[108])).
% 1.00/0.87 tff(110,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))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t62_tex_4')).
% 1.00/0.87 tff(111,plain,
% 1.00/0.87 (![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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.00/0.87 tff(112,plain,
% 1.00/0.87 (![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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.00/0.87 tff(113,plain,(
% 1.00/0.87 ![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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.87 inference(skolemize,[status(sab)],[112])).
% 1.00/0.87 tff(114,plain,
% 1.00/0.87 (![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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[113, 106])).
% 1.00/0.87 tff(115,plain,
% 1.00/0.87 (![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)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[114, 104])).
% 1.00/0.87 tff(116,plain,
% 1.00/0.87 (![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)))) | (~v4_pre_topc(B, A))))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[115, 99])).
% 1.00/0.87 tff(117,plain,
% 1.00/0.87 (v2_pre_topc(A!0)),
% 1.00/0.87 inference(and_elim,[status(thm)],[43])).
% 1.00/0.87 tff(118,plain,
% 1.00/0.87 (~v3_struct_0(A!0)),
% 1.00/0.87 inference(and_elim,[status(thm)],[43])).
% 1.00/0.87 tff(119,plain,
% 1.00/0.87 (((~![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)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v4_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)))) | (~v4_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(120,plain,
% 1.00/0.87 ((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)))) | (~v4_pre_topc(B, A!0)))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(121,plain,
% 1.00/0.87 (((~![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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))))),
% 1.00/0.87 inference(monotonicity,[status(thm)],[120])).
% 1.00/0.87 tff(122,plain,
% 1.00/0.87 (((~![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)))) | (~v4_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)))) | (~v4_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)))) | (~v4_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B)))),
% 1.00/0.87 inference(transitivity,[status(thm)],[121, 119])).
% 1.00/0.87 tff(123,plain,
% 1.00/0.87 ((~![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)))) | (~v4_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)))) | (~v4_pre_topc(B, A!0))))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(124,plain,
% 1.00/0.87 ((~![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)))) | (~v4_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.00/0.87 tff(125,plain,
% 1.00/0.87 (![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[124, 118, 117, 44, 116])).
% 1.00/0.87 tff(126,plain,
% 1.00/0.87 (v4_pre_topc(C!2, A!0)),
% 1.00/0.87 inference(or_elim,[status(thm)],[89])).
% 1.00/0.87 tff(127,plain,
% 1.00/0.87 (((~![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | ((~v4_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] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | (~v4_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))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(128,plain,
% 1.00/0.87 ((~![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | ((~v4_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))),
% 1.00/0.87 inference(quant_inst,[status(thm)],[])).
% 1.00/0.87 tff(129,plain,
% 1.00/0.87 ((~![B: $i] : ((~v4_pre_topc(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B))) | (~v4_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)),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.00/0.87 tff(130,plain,
% 1.00/0.87 (k3_tex_4(A!0, C!2) = C!2),
% 1.00/0.87 inference(unit_resolution,[status(thm)],[129, 126, 90, 125])).
% 1.00/0.87 tff(131,plain,
% 1.00/0.87 (C!2 = k3_tex_4(A!0, C!2)),
% 1.00/0.87 inference(symmetry,[status(thm)],[130])).
% 1.00/0.87 tff(132,plain,
% 1.00/0.87 (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))),
% 1.00/0.87 inference(monotonicity,[status(thm)],[131])).
% 1.00/0.87 tff(133,plain,
% 1.00/0.87 (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)),
% 1.00/0.87 inference(symmetry,[status(thm)],[132])).
% 1.00/0.87 tff(134,plain,
% 1.00/0.87 (^[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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(135,plain,
% 1.00/0.87 (![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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[134])).
% 1.00/0.87 tff(136,plain,
% 1.00/0.87 (^[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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(137,plain,
% 1.00/0.87 (![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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[136])).
% 1.00/0.87 tff(138,plain,
% 1.00/0.87 (^[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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(139,plain,
% 1.00/0.87 (![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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[138])).
% 1.00/0.87 tff(140,plain,
% 1.00/0.87 (![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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 1.00/0.87 inference(transitivity,[status(thm)],[139, 137])).
% 1.00/0.87 tff(141,plain,
% 1.00/0.87 (^[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(((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite(((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))), (((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))), rewrite(((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))) <=> ((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))), (((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))), ((((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))), rewrite((((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) <=> (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))), ((((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))) <=> (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(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)))) | (((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), 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))) | (~((~((~(C = k4_tsp_2(A, B))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(142,plain,
% 1.00/0.87 (![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[141])).
% 1.00/0.87 tff(143,plain,
% 1.00/0.87 (^[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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (~(~(tptp_fun_D_3(C, B, A) = u1_struct_0(B)))) & (~(~m1_subset_1(tptp_fun_D_3(C, B, A), 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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(144,plain,
% 1.00/0.87 (![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (~(~(tptp_fun_D_3(C, B, A) = u1_struct_0(B)))) & (~(~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[143])).
% 1.00/0.87 tff(145,plain,
% 1.00/0.87 (![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.00/0.87 inference(rewrite,[status(thm)],[])).
% 1.00/0.87 tff(146,plain,
% 1.00/0.87 (^[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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 1.00/0.87 inference(bind,[status(th)],[])).
% 1.00/0.87 tff(147,plain,
% 1.00/0.87 (![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)) <=> ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.00/0.87 inference(quant_intro,[status(thm)],[146])).
% 1.00/0.87 tff(148,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/sandbox/benchmark/theBenchmark.p','d12_tsp_2')).
% 1.00/0.87 tff(149,plain,
% 1.00/0.87 (![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.00/0.87 tff(150,plain,
% 1.00/0.87 (![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[149, 145])).
% 1.00/0.87 tff(151,plain,(
% 1.00/0.87 ![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (~(~(tptp_fun_D_3(C, B, A) = u1_struct_0(B)))) & (~(~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 1.00/0.87 inference(skolemize,[status(sab)],[150])).
% 1.00/0.87 tff(152,plain,
% 1.00/0.87 (![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] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & ((C = k4_tsp_2(A, B)) | ((~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))) & (tptp_fun_D_3(C, B, A) = u1_struct_0(B)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 1.00/0.87 inference(modus_ponens,[status(thm)],[151, 144])).
% 1.00/0.87 tff(153,plain,
% 1.00/0.87 (![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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[152, 142])).
% 1.00/0.88 tff(154,plain,
% 1.00/0.88 (![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))) | ![D: $i] : (![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))) | (~(D = u1_struct_0(B))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~((C = k4_tsp_2(A, B)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[153, 140])).
% 1.00/0.88 tff(155,plain,
% 1.00/0.88 (![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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[154, 135])).
% 1.00/0.88 tff(156,plain,
% 1.00/0.88 (((~![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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E)))))))))))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(157,plain,
% 1.00/0.88 ((~![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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E)))))))))))),
% 1.00/0.88 inference(quant_inst,[status(thm)],[])).
% 1.00/0.88 tff(158,plain,
% 1.00/0.88 ((~![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)) | (~((~(tptp_fun_D_3(C, B, A) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), tptp_fun_D_3(C, B, A), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~(C = k4_tsp_2(A, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.00/0.88 tff(159,plain,
% 1.00/0.88 (![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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[158, 118, 117, 44, 155])).
% 1.00/0.88 tff(160,plain,
% 1.00/0.88 (v2_tsp_2(B!1, A!0)),
% 1.00/0.88 inference(and_elim,[status(thm)],[43])).
% 1.00/0.88 tff(161,plain,
% 1.00/0.88 (~v3_struct_0(B!1)),
% 1.00/0.88 inference(and_elim,[status(thm)],[43])).
% 1.00/0.88 tff(162,plain,
% 1.00/0.88 (((~![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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))))) <=> ((~![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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(163,plain,
% 1.00/0.88 ((~![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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))))),
% 1.00/0.88 inference(quant_inst,[status(thm)],[])).
% 1.00/0.88 tff(164,plain,
% 1.00/0.88 ((~![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)) | (~((~(tptp_fun_D_3(C, B, A!0) = u1_struct_0(B))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B))) | ![D: $i] : ((~(D = u1_struct_0(B))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.00/0.88 tff(165,plain,
% 1.00/0.88 (![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)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[164, 161, 160, 51, 159])).
% 1.00/0.88 tff(166,plain,
% 1.00/0.88 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 1.00/0.88 inference(bind,[status(th)],[])).
% 1.00/0.88 tff(167,plain,
% 1.00/0.88 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.00/0.88 inference(quant_intro,[status(thm)],[166])).
% 1.00/0.88 tff(168,plain,
% 1.00/0.88 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 1.00/0.88 inference(bind,[status(th)],[])).
% 1.00/0.88 tff(169,plain,
% 1.00/0.88 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.00/0.88 inference(quant_intro,[status(thm)],[168])).
% 1.00/0.88 tff(170,plain,
% 1.00/0.88 (![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))))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(171,plain,
% 1.00/0.88 (^[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))))))),
% 1.00/0.88 inference(bind,[status(th)],[])).
% 1.00/0.88 tff(172,plain,
% 1.00/0.88 (![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))))),
% 1.00/0.88 inference(quant_intro,[status(thm)],[171])).
% 1.00/0.88 tff(173,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/sandbox/benchmark/theBenchmark.p','dt_k1_tsp_2')).
% 1.00/0.88 tff(174,plain,
% 1.00/0.88 (![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))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.00/0.88 tff(175,plain,
% 1.00/0.88 (![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))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[174, 170])).
% 1.00/0.88 tff(176,plain,(
% 1.00/0.88 ![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))))),
% 1.00/0.88 inference(skolemize,[status(sab)],[175])).
% 1.00/0.88 tff(177,plain,
% 1.00/0.88 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[176, 169])).
% 1.00/0.88 tff(178,plain,
% 1.00/0.88 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[177, 167])).
% 1.00/0.88 tff(179,plain,
% 1.00/0.88 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(180,plain,
% 1.00/0.88 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(181,plain,
% 1.00/0.88 ((~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.00/0.88 inference(rewrite,[status(thm)],[])).
% 1.00/0.88 tff(182,plain,
% 1.00/0.88 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.00/0.88 inference(monotonicity,[status(thm)],[181])).
% 1.00/0.88 tff(183,plain,
% 1.00/0.88 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.00/0.88 inference(transitivity,[status(thm)],[182, 180])).
% 1.00/0.88 tff(184,plain,
% 1.00/0.88 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 1.00/0.88 inference(monotonicity,[status(thm)],[183])).
% 1.00/0.88 tff(185,plain,
% 1.00/0.88 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.00/0.88 inference(transitivity,[status(thm)],[184, 179])).
% 1.00/0.88 tff(186,plain,
% 1.00/0.88 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 1.00/0.88 inference(quant_inst,[status(thm)],[])).
% 1.00/0.88 tff(187,plain,
% 1.00/0.88 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.00/0.88 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.00/0.88 tff(188,plain,
% 1.00/0.88 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[187, 118, 117, 44, 161, 160, 178])).
% 1.00/0.88 tff(189,plain,
% 1.00/0.88 (~((~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))))),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[188, 54])).
% 1.00/0.88 tff(190,plain,
% 1.00/0.88 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.00/0.88 inference(tautology,[status(thm)],[])).
% 1.00/0.88 tff(191,plain,
% 1.00/0.88 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[190, 189])).
% 1.00/0.88 tff(192,plain,
% 1.00/0.88 (((~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)))) | v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 1.00/0.88 inference(tautology,[status(thm)],[])).
% 1.00/0.88 tff(193,plain,
% 1.00/0.88 (v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 1.00/0.88 inference(unit_resolution,[status(thm)],[192, 189])).
% 1.00/0.88 tff(194,plain,
% 1.00/0.88 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.00/0.89 inference(tautology,[status(thm)],[])).
% 1.00/0.89 tff(195,plain,
% 1.00/0.89 (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.00/0.89 inference(unit_resolution,[status(thm)],[194, 189])).
% 1.00/0.89 tff(196,plain,
% 1.00/0.89 (((~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))),
% 1.00/0.89 inference(tautology,[status(thm)],[])).
% 1.00/0.89 tff(197,plain,
% 1.00/0.89 (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 1.00/0.89 inference(unit_resolution,[status(thm)],[196, 189])).
% 1.00/0.89 tff(198,plain,
% 1.00/0.89 (((~![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)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(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), tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(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_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(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), tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(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_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(199,plain,
% 1.00/0.89 ((~![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)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(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), tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(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_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))))),
% 1.00/0.89 inference(quant_inst,[status(thm)],[])).
% 1.00/0.89 tff(200,plain,
% 1.00/0.89 ((~![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)) | (~((~(tptp_fun_D_3(C, B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), tptp_fun_D_3(C, B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~(C = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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)) | (~((~(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(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), tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(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_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))),
% 1.00/0.89 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.00/0.89 tff(201,plain,
% 1.00/0.89 (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(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), tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(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_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))),
% 1.00/0.89 inference(unit_resolution,[status(thm)],[200, 197, 195, 193, 191, 165])).
% 1.00/0.89 tff(202,plain,
% 1.00/0.89 (((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0) = u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(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), tptp_fun_D_3(k1_tsp_2(A!0, B!1), B!1, A!0), k3_tex_4(A!0, tptp_fun_E_4(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_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))),
% 1.00/0.89 inference(tautology,[status(thm)],[])).
% 1.00/0.89 tff(203,plain,
% 1.00/0.89 ((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))),
% 1.00/0.89 inference(unit_resolution,[status(thm)],[202, 201])).
% 1.00/0.89 tff(204,plain,
% 1.00/0.89 (^[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)) | (~v2_pre_topc(A)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))),
% 1.00/0.89 inference(bind,[status(th)],[])).
% 1.00/0.89 tff(205,plain,
% 1.00/0.89 (![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 1.00/0.89 inference(quant_intro,[status(thm)],[204])).
% 1.00/0.89 tff(206,plain,
% 1.00/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (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)) | (~v2_pre_topc(A)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))))),
% 1.00/0.89 inference(bind,[status(th)],[])).
% 1.00/0.89 tff(207,plain,
% 1.00/0.89 (![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 1.00/0.89 inference(quant_intro,[status(thm)],[206])).
% 1.00/0.89 tff(208,plain,
% 1.00/0.89 (![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)))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(209,plain,
% 1.00/0.89 (^[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)))))),
% 1.00/0.89 inference(bind,[status(th)],[])).
% 1.00/0.89 tff(210,plain,
% 1.00/0.89 (![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)))),
% 1.00/0.89 inference(quant_intro,[status(thm)],[209])).
% 1.00/0.89 tff(211,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/sandbox/benchmark/theBenchmark.p','redefinition_k4_tsp_2')).
% 1.00/0.89 tff(212,plain,
% 1.00/0.89 (![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)))),
% 1.00/0.89 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.00/0.89 tff(213,plain,
% 1.00/0.89 (![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)))),
% 1.00/0.89 inference(modus_ponens,[status(thm)],[212, 208])).
% 1.00/0.89 tff(214,plain,(
% 1.00/0.89 ![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)))),
% 1.00/0.89 inference(skolemize,[status(sab)],[213])).
% 1.00/0.89 tff(215,plain,
% 1.00/0.89 (![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 1.00/0.89 inference(modus_ponens,[status(thm)],[214, 207])).
% 1.00/0.89 tff(216,plain,
% 1.00/0.89 (![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 1.00/0.89 inference(modus_ponens,[status(thm)],[215, 205])).
% 1.00/0.89 tff(217,plain,
% 1.00/0.89 (((~![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(218,plain,
% 1.03/0.89 ((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)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(219,plain,
% 1.03/0.89 (((~![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))))),
% 1.03/0.89 inference(monotonicity,[status(thm)],[218])).
% 1.03/0.89 tff(220,plain,
% 1.03/0.89 (((~![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 1.03/0.89 inference(transitivity,[status(thm)],[219, 217])).
% 1.03/0.89 tff(221,plain,
% 1.03/0.89 ((~![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))),
% 1.03/0.89 inference(quant_inst,[status(thm)],[])).
% 1.03/0.89 tff(222,plain,
% 1.03/0.89 ((~![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)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.03/0.89 tff(223,plain,
% 1.03/0.89 ((k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[222, 118, 117, 44, 161, 160, 216])).
% 1.03/0.89 tff(224,plain,
% 1.03/0.89 (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[223, 54])).
% 1.03/0.89 tff(225,plain,
% 1.03/0.89 (k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)),
% 1.03/0.89 inference(symmetry,[status(thm)],[224])).
% 1.03/0.89 tff(226,plain,
% 1.03/0.89 ((~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, 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))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))),
% 1.03/0.89 inference(tautology,[status(thm)],[])).
% 1.03/0.89 tff(227,plain,
% 1.03/0.89 ((~((~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))) | ![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[226, 225])).
% 1.03/0.89 tff(228,plain,
% 1.03/0.89 (![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[227, 203])).
% 1.03/0.89 tff(229,plain,
% 1.03/0.89 (((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | ((~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))))) <=> ((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(230,plain,
% 1.03/0.89 (($false | (~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)))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(231,plain,
% 1.03/0.89 ((~$true) <=> $false),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(232,plain,
% 1.03/0.89 ((u1_struct_0(B!1) = u1_struct_0(B!1)) <=> $true),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(233,plain,
% 1.03/0.89 ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) <=> (~$true)),
% 1.03/0.89 inference(monotonicity,[status(thm)],[232])).
% 1.03/0.89 tff(234,plain,
% 1.03/0.89 ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) <=> $false),
% 1.03/0.89 inference(transitivity,[status(thm)],[233, 231])).
% 1.03/0.89 tff(235,plain,
% 1.03/0.89 (((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) <=> ($false | (~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))))),
% 1.03/0.89 inference(monotonicity,[status(thm)],[234])).
% 1.03/0.89 tff(236,plain,
% 1.03/0.89 (((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![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(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))))),
% 1.03/0.90 inference(transitivity,[status(thm)],[235, 230])).
% 1.03/0.90 tff(237,plain,
% 1.03/0.90 (((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![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))))) <=> ((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | ((~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)))))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[236])).
% 1.03/0.90 tff(238,plain,
% 1.03/0.90 (((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![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))))) <=> ((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | (~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))))),
% 1.03/0.90 inference(transitivity,[status(thm)],[237, 229])).
% 1.03/0.90 tff(239,plain,
% 1.03/0.90 ((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | ((~(u1_struct_0(B!1) = u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![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))))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(240,plain,
% 1.03/0.90 ((~![D: $i] : ((~(D = u1_struct_0(B!1))) | (~m1_subset_1(D, 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), D, k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))) | (~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)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.03/0.90 tff(241,plain,
% 1.03/0.90 (![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)))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[240, 75, 228])).
% 1.03/0.90 tff(242,plain,
% 1.03/0.90 (((~![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)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(243,plain,
% 1.03/0.90 ((~![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)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(244,plain,
% 1.03/0.90 ((~![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))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.03/0.90 tff(245,plain,
% 1.03/0.90 (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)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[244, 90, 241])).
% 1.03/0.90 tff(246,plain,
% 1.03/0.90 (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))),
% 1.03/0.90 inference(symmetry,[status(thm)],[245])).
% 1.03/0.90 tff(247,plain,
% 1.03/0.90 (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)),
% 1.03/0.90 inference(monotonicity,[status(thm)],[225])).
% 1.03/0.90 tff(248,plain,
% 1.03/0.90 (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)),
% 1.03/0.90 inference(symmetry,[status(thm)],[247])).
% 1.03/0.90 tff(249,plain,
% 1.03/0.90 (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))),
% 1.03/0.90 inference(transitivity,[status(thm)],[248, 246, 133, 97, 10])).
% 1.03/0.90 tff(250,plain,
% 1.03/0.90 (^[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)))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(251,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[250])).
% 1.03/0.90 tff(252,plain,
% 1.03/0.90 (^[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)))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(253,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[252])).
% 1.03/0.90 tff(254,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(transitivity,[status(thm)],[253, 251])).
% 1.03/0.90 tff(255,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(256,plain,
% 1.03/0.90 (^[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))))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(257,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[256])).
% 1.03/0.90 tff(258,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_tsp_1')).
% 1.03/0.90 tff(259,plain,
% 1.03/0.90 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.03/0.90 tff(260,plain,
% 1.03/0.90 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[259, 255])).
% 1.03/0.90 tff(261,plain,(
% 1.03/0.90 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.03/0.90 inference(skolemize,[status(sab)],[260])).
% 1.03/0.90 tff(262,plain,
% 1.03/0.90 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[261, 254])).
% 1.03/0.90 tff(263,plain,
% 1.03/0.90 (((~![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))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(264,plain,
% 1.03/0.90 ((~![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))))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(265,plain,
% 1.03/0.90 ((~![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)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.03/0.90 tff(266,plain,
% 1.03/0.90 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[265, 44, 262])).
% 1.03/0.90 tff(267,plain,
% 1.03/0.90 (((~![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)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(268,plain,
% 1.03/0.90 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(269,plain,
% 1.03/0.90 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.03/0.90 tff(270,plain,
% 1.03/0.90 (l1_pre_topc(B!1)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[269, 51, 266])).
% 1.03/0.90 tff(271,plain,
% 1.03/0.90 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(272,plain,
% 1.03/0.90 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[271])).
% 1.03/0.90 tff(273,plain,
% 1.03/0.90 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(274,plain,
% 1.03/0.90 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(275,plain,
% 1.03/0.90 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[274])).
% 1.03/0.90 tff(276,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 1.03/0.90 tff(277,plain,
% 1.03/0.90 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.03/0.90 tff(278,plain,
% 1.03/0.90 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[277, 273])).
% 1.03/0.90 tff(279,plain,(
% 1.03/0.90 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(skolemize,[status(sab)],[278])).
% 1.03/0.90 tff(280,plain,
% 1.03/0.90 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[279, 272])).
% 1.03/0.90 tff(281,plain,
% 1.03/0.90 (((~![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)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(282,plain,
% 1.03/0.90 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(283,plain,
% 1.03/0.90 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.03/0.90 tff(284,plain,
% 1.03/0.90 (l1_struct_0(B!1)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[283, 280, 270])).
% 1.03/0.90 tff(285,plain,
% 1.03/0.90 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A)) | (~l1_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)))))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(286,plain,
% 1.03/0.90 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A)) | (~l1_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))))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[285])).
% 1.03/0.90 tff(287,plain,
% 1.03/0.90 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(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)) | (~v2_pre_topc(A)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_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))))))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(288,plain,
% 1.03/0.90 (![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)) | (~v2_pre_topc(A)) | (~l1_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))))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[287])).
% 1.03/0.90 tff(289,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(290,plain,
% 1.03/0.90 (^[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))))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(291,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[290])).
% 1.03/0.90 tff(292,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/sandbox/benchmark/theBenchmark.p','dt_k4_tsp_2')).
% 1.03/0.90 tff(293,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[292, 291])).
% 1.03/0.90 tff(294,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[293, 289])).
% 1.03/0.90 tff(295,plain,(
% 1.03/0.90 ![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))))),
% 1.03/0.90 inference(skolemize,[status(sab)],[294])).
% 1.03/0.90 tff(296,plain,
% 1.03/0.90 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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))))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[295, 288])).
% 1.03/0.90 tff(297,plain,
% 1.03/0.90 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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))))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[296, 286])).
% 1.03/0.90 tff(298,plain,
% 1.03/0.90 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A)) | (~l1_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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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))))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(299,plain,
% 1.03/0.90 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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))))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(300,plain,
% 1.03/0.90 ((~((~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)))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(301,plain,
% 1.03/0.90 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A!0)) | (~l1_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))))))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[300])).
% 1.03/0.90 tff(302,plain,
% 1.03/0.90 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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))))))),
% 1.03/0.90 inference(transitivity,[status(thm)],[301, 299])).
% 1.03/0.90 tff(303,plain,
% 1.03/0.90 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A!0)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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)))))))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[302])).
% 1.03/0.90 tff(304,plain,
% 1.03/0.90 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A!0)) | (~l1_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)) | (~v2_pre_topc(A)) | (~l1_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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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))))))),
% 1.03/0.90 inference(transitivity,[status(thm)],[303, 298])).
% 1.03/0.90 tff(305,plain,
% 1.03/0.90 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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)) | (~v2_pre_topc(A!0)) | (~l1_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))))))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(306,plain,
% 1.03/0.90 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(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) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(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)))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.03/0.90 tff(307,plain,
% 1.03/0.90 ((~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)))))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[306, 118, 117, 44, 161, 160, 297])).
% 1.03/0.90 tff(308,plain,
% 1.03/0.90 (~((~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))))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[307, 54])).
% 1.03/0.90 tff(309,plain,
% 1.03/0.90 (((~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))),
% 1.03/0.90 inference(tautology,[status(thm)],[])).
% 1.03/0.90 tff(310,plain,
% 1.03/0.90 (v1_funct_1(k4_tsp_2(A!0, B!1))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[309, 308])).
% 1.03/0.90 tff(311,plain,
% 1.03/0.90 (((~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))),
% 1.03/0.90 inference(tautology,[status(thm)],[])).
% 1.03/0.90 tff(312,plain,
% 1.03/0.90 (v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[311, 308])).
% 1.03/0.90 tff(313,plain,
% 1.03/0.90 (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))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[225])).
% 1.03/0.90 tff(314,plain,
% 1.03/0.90 (^[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)))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(315,plain,
% 1.03/0.90 (![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))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[314])).
% 1.03/0.90 tff(316,plain,
% 1.03/0.90 (![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))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(317,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 1.03/0.90 tff(318,plain,
% 1.03/0.90 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[317, 316])).
% 1.03/0.90 tff(319,plain,(
% 1.03/0.90 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.03/0.90 inference(skolemize,[status(sab)],[318])).
% 1.03/0.90 tff(320,plain,
% 1.03/0.90 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.03/0.90 tff(321,plain,
% 1.03/0.90 ((~![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)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(322,plain,
% 1.03/0.90 (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))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[321, 320])).
% 1.03/0.90 tff(323,plain,
% 1.03/0.90 ((~(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))),
% 1.03/0.90 inference(tautology,[status(thm)],[])).
% 1.03/0.90 tff(324,plain,
% 1.03/0.90 ((~(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))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[323, 191])).
% 1.03/0.90 tff(325,plain,
% 1.03/0.90 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[324, 322])).
% 1.03/0.90 tff(326,plain,
% 1.03/0.90 (m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[325, 313])).
% 1.03/0.90 tff(327,plain,
% 1.03/0.90 (((~![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)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(328,plain,
% 1.03/0.90 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(329,plain,
% 1.03/0.90 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.03/0.90 tff(330,plain,
% 1.03/0.90 (l1_struct_0(A!0)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[329, 44, 280])).
% 1.03/0.90 tff(331,plain,
% 1.03/0.90 (^[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)))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(332,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[331])).
% 1.03/0.90 tff(333,plain,
% 1.03/0.90 (^[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))))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(334,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[333])).
% 1.03/0.90 tff(335,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(336,plain,
% 1.03/0.90 (^[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))))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(337,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[336])).
% 1.03/0.90 tff(338,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/sandbox/benchmark/theBenchmark.p','dt_k4_pre_topc')).
% 1.03/0.90 tff(339,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.03/0.90 tff(340,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[339, 335])).
% 1.03/0.90 tff(341,plain,(
% 1.03/0.90 ![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))))),
% 1.03/0.90 inference(skolemize,[status(sab)],[340])).
% 1.03/0.90 tff(342,plain,
% 1.03/0.90 (![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))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[341, 334])).
% 1.03/0.91 tff(343,plain,
% 1.03/0.91 (![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))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[342, 332])).
% 1.03/0.91 tff(344,plain,
% 1.03/0.91 (((~![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))))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(345,plain,
% 1.03/0.91 ((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))))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(346,plain,
% 1.03/0.91 (((~![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)))))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[345])).
% 1.03/0.91 tff(347,plain,
% 1.03/0.91 (((~![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))))),
% 1.03/0.91 inference(transitivity,[status(thm)],[346, 344])).
% 1.03/0.91 tff(348,plain,
% 1.03/0.91 ((~![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))))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(349,plain,
% 1.03/0.91 ((~![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)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.03/0.91 tff(350,plain,
% 1.03/0.91 ((~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)))),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[349, 343, 330])).
% 1.03/0.91 tff(351,plain,
% 1.03/0.91 (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)))),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[350, 326, 312, 310, 284])).
% 1.03/0.91 tff(352,plain,
% 1.03/0.91 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))))))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(353,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[352])).
% 1.03/0.91 tff(354,plain,
% 1.03/0.91 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(355,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[354])).
% 1.03/0.91 tff(356,plain,
% 1.03/0.91 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(357,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[356])).
% 1.03/0.91 tff(358,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.03/0.91 inference(transitivity,[status(thm)],[357, 355])).
% 1.03/0.91 tff(359,plain,
% 1.03/0.91 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(360,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[359])).
% 1.03/0.91 tff(361,plain,
% 1.03/0.91 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | ((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | ((~(~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))))) & ((v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(362,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | ((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | ((~(~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))))) & ((v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[361])).
% 1.03/0.91 tff(363,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_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)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(364,plain,
% 1.03/0.91 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))) <=> (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))), ((l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> (l1_pre_topc(B) => (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), rewrite((l1_pre_topc(B) => (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))), ((l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))))), (![B: $i] : (l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))) <=> ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), ((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), ((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(365,plain,
% 1.03/0.91 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_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)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[364])).
% 1.03/0.91 tff(366,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) => (m2_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))) => (v4_pre_topc(C, B) <=> ?[D: $i] : ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A)) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tsp_1')).
% 1.03/0.91 tff(367,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[366, 365])).
% 1.03/0.91 tff(368,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (m2_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)))) | (v4_pre_topc(C, B) <=> ?[D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B))))))))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[367, 363])).
% 1.03/0.91 tff(369,plain,(
% 1.03/0.91 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | ((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | ((~(~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))))) & ((v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))),
% 1.03/0.91 inference(skolemize,[status(sab)],[368])).
% 1.03/0.91 tff(370,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (((~m2_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)))) | (((~v4_pre_topc(C, B)) | (m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_5(C, B, A), A) & (C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B))))) & (v4_pre_topc(C, B) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (C = k3_xboole_0(D, u1_struct_0(B)))))))))) & (m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B))) & (v4_pre_topc(tptp_fun_C_6(B, A), B) | (m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(tptp_fun_D_7(B, A), A) & (tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B))))) & ((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : (~(m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D, A) & (tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[369, 362])).
% 1.03/0.91 tff(371,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[370, 360])).
% 1.03/0.91 tff(372,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B))))))))))))))) | (~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B)))))))))))))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[371, 358])).
% 1.03/0.91 tff(373,plain,
% 1.03/0.91 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[372, 353])).
% 1.03/0.91 tff(374,plain,
% 1.03/0.91 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)))))))))))))))))))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(375,plain,
% 1.03/0.91 (((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_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)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)))))))))))))))))))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(376,plain,
% 1.03/0.91 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_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)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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))))))))))))))))))))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[375])).
% 1.03/0.92 tff(377,plain,
% 1.03/0.92 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_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)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)))))))))))))))))))),
% 1.03/0.92 inference(transitivity,[status(thm)],[376, 374])).
% 1.03/0.92 tff(378,plain,
% 1.03/0.92 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(D, A!0)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(379,plain,
% 1.03/0.92 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~((~m1_subset_1(tptp_fun_C_6(B, A), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A), A)) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(tptp_fun_D_7(B, A), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A), k1_zfmisc_1(u1_struct_0(A)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A), B)) | ![D: $i] : ((~v4_pre_topc(D, A)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~(tptp_fun_C_6(B, A) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A), A)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(D, A)) | (~(C = k3_xboole_0(D, u1_struct_0(B)))))))))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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))))))))))))))))))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.03/0.92 tff(380,plain,
% 1.03/0.92 (![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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))))))))))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[379, 44, 373])).
% 1.03/0.92 tff(381,plain,
% 1.03/0.92 (((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)) | (~((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)) | (~((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))))))))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(382,plain,
% 1.03/0.92 ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)) | (~((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))))))))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(383,plain,
% 1.03/0.92 ((~![B: $i] : ((~l1_pre_topc(B)) | (~((~(m2_tsp_1(B, A!0) | (~r1_tarski(u1_struct_0(B), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B, A!0), k1_zfmisc_1(u1_struct_0(B)))) | (~(v4_pre_topc(tptp_fun_C_6(B, A!0), B) | (~((~v4_pre_topc(tptp_fun_D_7(B, A!0), A!0)) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(tptp_fun_D_7(B, A!0), u1_struct_0(B)))) | (~m1_subset_1(tptp_fun_D_7(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B, A!0), B)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B, A!0) = k3_xboole_0(D, u1_struct_0(B))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B)) | (~((~m1_subset_1(tptp_fun_D_5(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B, A!0), u1_struct_0(B)))))))) | (~(v4_pre_topc(C, B) | ![D: $i] : ((~v4_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)) | (~((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))))))))))))))))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[382, 381])).
% 1.03/0.92 tff(384,plain,
% 1.03/0.92 ((~l1_pre_topc(B!1)) | (~((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))))))))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[383, 380])).
% 1.03/0.92 tff(385,plain,
% 1.03/0.92 (~((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[384, 270])).
% 1.03/0.92 tff(386,plain,
% 1.03/0.92 (((~(m2_tsp_1(B!1, A!0) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~m1_subset_1(tptp_fun_C_6(B!1, A!0), k1_zfmisc_1(u1_struct_0(B!1)))) | (~(v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1) | (~((~v4_pre_topc(tptp_fun_D_7(B!1, A!0), A!0)) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(tptp_fun_D_7(B!1, A!0), u1_struct_0(B!1)))) | (~m1_subset_1(tptp_fun_D_7(B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~((~v4_pre_topc(tptp_fun_C_6(B!1, A!0), B!1)) | ![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(tptp_fun_C_6(B!1, A!0) = k3_xboole_0(D, u1_struct_0(B!1))))))))))) | (~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))))))))))))))) | ((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))))),
% 1.03/0.92 inference(tautology,[status(thm)],[])).
% 1.03/0.92 tff(387,plain,
% 1.03/0.92 ((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[386, 385])).
% 1.03/0.92 tff(388,plain,
% 1.03/0.92 ((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))))) | (~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))))))))))))),
% 1.03/0.92 inference(tautology,[status(thm)],[])).
% 1.03/0.92 tff(389,plain,
% 1.03/0.92 ((~((~m2_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))))) | (~((~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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[388, 51])).
% 1.03/0.92 tff(390,plain,
% 1.03/0.92 (~((~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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[389, 387])).
% 1.03/0.92 tff(391,plain,
% 1.03/0.92 (((~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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))),
% 1.03/0.92 inference(tautology,[status(thm)],[])).
% 1.03/0.92 tff(392,plain,
% 1.03/0.92 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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))))))))))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[391, 390])).
% 1.03/0.92 tff(393,plain,
% 1.03/0.92 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))) | (~((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))) | (~((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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))))))))))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(394,plain,
% 1.03/0.92 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))) | (~((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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))))))))))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(395,plain,
% 1.03/0.93 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~((~v4_pre_topc(C, B!1)) | (~((~m1_subset_1(tptp_fun_D_5(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(tptp_fun_D_5(C, B!1, A!0), A!0)) | (~(C = k3_xboole_0(tptp_fun_D_5(C, B!1, A!0), u1_struct_0(B!1)))))))) | (~(v4_pre_topc(C, B!1) | ![D: $i] : ((~v4_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)))) | (~((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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)))))))))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.03/0.93 tff(396,plain,
% 1.03/0.93 ((~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)))) | (~((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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)))))))))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[395, 392])).
% 1.03/0.93 tff(397,plain,
% 1.03/0.93 (~((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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))))))))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[396, 351])).
% 1.03/0.93 tff(398,plain,
% 1.03/0.93 (((~((~v4_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_5(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)))) | (~v4_pre_topc(tptp_fun_D_5(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_5(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)))))))) | (~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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)))))))) | (v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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))))))),
% 1.07/0.93 inference(tautology,[status(thm)],[])).
% 1.07/0.93 tff(399,plain,
% 1.07/0.93 (v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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)))))),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[398, 397])).
% 1.07/0.93 tff(400,plain,
% 1.07/0.93 (~v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1)),
% 1.07/0.93 inference(or_elim,[status(thm)],[89])).
% 1.07/0.93 tff(401,plain,
% 1.07/0.93 ((~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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))))))) | v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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)))))),
% 1.07/0.93 inference(tautology,[status(thm)],[])).
% 1.07/0.93 tff(402,plain,
% 1.07/0.93 ((~(v4_pre_topc(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), B!1) | ![D: $i] : ((~v4_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] : ((~v4_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)))))),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[401, 400])).
% 1.07/0.93 tff(403,plain,
% 1.07/0.93 (![D: $i] : ((~v4_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)))))),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[402, 399])).
% 1.07/0.93 tff(404,plain,
% 1.07/0.93 (((~![D: $i] : ((~v4_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)))))) | ((~v4_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] : ((~v4_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)))))) | (~v4_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)))))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(405,plain,
% 1.07/0.93 ((~![D: $i] : ((~v4_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)))))) | ((~v4_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)))))),
% 1.07/0.93 inference(quant_inst,[status(thm)],[])).
% 1.07/0.93 tff(406,plain,
% 1.07/0.93 ((~![D: $i] : ((~v4_pre_topc(D, A!0)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(D, u1_struct_0(B!1)))))) | (~v4_pre_topc(C!2, A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1))))),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.07/0.94 tff(407,plain,
% 1.07/0.94 (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(C!2, u1_struct_0(B!1)))),
% 1.07/0.94 inference(unit_resolution,[status(thm)],[406, 126, 90, 403])).
% 1.07/0.94 tff(408,plain,
% 1.07/0.94 ($false),
% 1.07/0.94 inference(unit_resolution,[status(thm)],[407, 249])).
% 1.07/0.94 % SZS output end Proof
%------------------------------------------------------------------------------