TSTP Solution File: TOP035+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP035+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 30 01:55:58 EDT 2022
% Result : Theorem 0.56s 0.59s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP035+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.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 11:16:50 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.
% 0.56/0.59 % SZS status Theorem
% 0.56/0.59 % SZS output start Proof
% 0.56/0.59 tff(k6_pre_topc_type, type, (
% 0.56/0.59 k6_pre_topc: ( $i * $i ) > $i)).
% 0.56/0.59 tff(k1_struct_0_type, type, (
% 0.56/0.59 k1_struct_0: ( $i * $i ) > $i)).
% 0.56/0.59 tff(tptp_fun_C_2_type, type, (
% 0.56/0.59 tptp_fun_C_2: $i)).
% 0.56/0.59 tff(tptp_fun_A_0_type, type, (
% 0.56/0.59 tptp_fun_A_0: $i)).
% 0.56/0.59 tff(k5_pre_topc_type, type, (
% 0.56/0.59 k5_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 0.56/0.59 tff(tptp_fun_D_3_type, type, (
% 0.56/0.59 tptp_fun_D_3: $i)).
% 0.56/0.59 tff(tptp_fun_B_1_type, type, (
% 0.56/0.59 tptp_fun_B_1: $i)).
% 0.56/0.59 tff(k1_tsp_2_type, type, (
% 0.56/0.59 k1_tsp_2: ( $i * $i ) > $i)).
% 0.56/0.59 tff(m1_subset_1_type, type, (
% 0.56/0.59 m1_subset_1: ( $i * $i ) > $o)).
% 0.56/0.59 tff(u1_struct_0_type, type, (
% 0.56/0.59 u1_struct_0: $i > $i)).
% 0.56/0.59 tff(m2_tsp_1_type, type, (
% 0.56/0.59 m2_tsp_1: ( $i * $i ) > $o)).
% 0.56/0.59 tff(v2_tsp_2_type, type, (
% 0.56/0.59 v2_tsp_2: ( $i * $i ) > $o)).
% 0.56/0.59 tff(v3_struct_0_type, type, (
% 0.56/0.59 v3_struct_0: $i > $o)).
% 0.56/0.59 tff(l1_pre_topc_type, type, (
% 0.56/0.59 l1_pre_topc: $i > $o)).
% 0.56/0.59 tff(v2_pre_topc_type, type, (
% 0.56/0.59 v2_pre_topc: $i > $o)).
% 0.56/0.59 tff(v3_borsuk_1_type, type, (
% 0.56/0.59 v3_borsuk_1: ( $i * $i * $i ) > $o)).
% 0.56/0.59 tff(m2_relset_1_type, type, (
% 0.56/0.59 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.56/0.59 tff(v5_pre_topc_type, type, (
% 0.56/0.59 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 0.56/0.59 tff(v1_funct_2_type, type, (
% 0.56/0.59 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.56/0.59 tff(v1_funct_1_type, type, (
% 0.56/0.59 v1_funct_1: $i > $o)).
% 0.56/0.59 tff(m1_pre_topc_type, type, (
% 0.56/0.59 m1_pre_topc: ( $i * $i ) > $o)).
% 0.56/0.59 tff(1,plain,
% 0.56/0.59 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(2,plain,
% 0.56/0.59 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(3,plain,
% 0.56/0.59 (((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(4,plain,
% 0.56/0.59 ((~(~((~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))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(5,plain,
% 0.56/0.59 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))) <=> (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))))),
% 0.56/0.59 inference(monotonicity,[status(thm)],[4, 3])).
% 0.56/0.59 tff(6,plain,
% 0.56/0.59 (((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))),
% 0.56/0.59 inference(transitivity,[status(thm)],[5, 2])).
% 0.56/0.59 tff(7,plain,
% 0.56/0.59 ((~(~((~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))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(8,plain,
% 0.56/0.59 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))))),
% 0.56/0.59 inference(monotonicity,[status(thm)],[7, 6])).
% 0.56/0.59 tff(9,plain,
% 0.56/0.59 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))),
% 0.56/0.59 inference(transitivity,[status(thm)],[8, 1])).
% 0.56/0.59 tff(10,plain,
% 0.56/0.59 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))))))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(11,plain,
% 0.56/0.59 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => ((C = D) => (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))))))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(12,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => ((C = D) => (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_tsp_2')).
% 0.56/0.60 tff(13,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.56/0.60 tff(14,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.56/0.60 tff(15,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.56/0.60 tff(16,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.56/0.60 tff(17,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.56/0.60 tff(18,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.56/0.60 tff(19,plain,
% 0.56/0.60 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, C))) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.56/0.60 tff(20,plain,
% 0.56/0.60 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.56/0.60 tff(21,plain,
% 0.56/0.60 (~((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(22,plain,
% 0.56/0.60 (C!2 = D!3),
% 0.56/0.60 inference(or_elim,[status(thm)],[21])).
% 0.56/0.60 tff(23,plain,
% 0.56/0.60 (D!3 = C!2),
% 0.56/0.60 inference(symmetry,[status(thm)],[22])).
% 0.56/0.60 tff(24,plain,
% 0.56/0.60 (k1_struct_0(A!0, D!3) = k1_struct_0(A!0, C!2)),
% 0.56/0.60 inference(monotonicity,[status(thm)],[23])).
% 0.56/0.60 tff(25,plain,
% 0.56/0.60 (k1_struct_0(A!0, C!2) = k1_struct_0(A!0, D!3)),
% 0.56/0.60 inference(symmetry,[status(thm)],[24])).
% 0.56/0.60 tff(26,plain,
% 0.56/0.60 (k6_pre_topc(A!0, k1_struct_0(A!0, C!2)) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))),
% 0.56/0.60 inference(monotonicity,[status(thm)],[25])).
% 0.56/0.60 tff(27,plain,
% 0.56/0.60 (k6_pre_topc(A!0, k1_struct_0(A!0, D!3)) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))),
% 0.56/0.60 inference(symmetry,[status(thm)],[26])).
% 0.56/0.60 tff(28,plain,
% 0.56/0.60 (^[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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(29,plain,
% 0.56/0.60 (![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[28])).
% 0.56/0.60 tff(30,plain,
% 0.56/0.60 (^[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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(31,plain,
% 0.56/0.60 (![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[30])).
% 0.56/0.60 tff(32,plain,
% 0.56/0.60 (![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.60 inference(transitivity,[status(thm)],[31, 29])).
% 0.56/0.60 tff(33,plain,
% 0.56/0.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, 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)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), 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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(34,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[33])).
% 0.56/0.60 tff(35,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(36,plain,
% 0.56/0.60 (^[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))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, 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))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))))), 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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(37,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[36])).
% 0.56/0.60 tff(38,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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_tsp_2')).
% 0.56/0.60 tff(39,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.56/0.60 tff(40,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.56/0.60 tff(41,plain,(
% 0.56/0.60 ![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 = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)))))),
% 0.56/0.60 inference(skolemize,[status(sab)],[40])).
% 0.56/0.60 tff(42,plain,
% 0.56/0.60 (![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.56/0.60 tff(43,plain,
% 0.56/0.60 (![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.56/0.60 tff(44,plain,
% 0.56/0.60 (l1_pre_topc(A!0)),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(45,plain,
% 0.56/0.60 (v2_pre_topc(A!0)),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(46,plain,
% 0.56/0.60 (~v3_struct_0(A!0)),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(47,plain,
% 0.56/0.60 (((~![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | 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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(48,plain,
% 0.56/0.60 ((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] : (((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B)))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(49,plain,
% 0.56/0.60 (((~![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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] : (((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))))),
% 0.56/0.60 inference(monotonicity,[status(thm)],[48])).
% 0.56/0.60 tff(50,plain,
% 0.56/0.60 (((~![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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] : (((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | 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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))),
% 0.56/0.60 inference(transitivity,[status(thm)],[49, 47])).
% 0.56/0.60 tff(51,plain,
% 0.56/0.60 ((~![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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] : (((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)) | (~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))))))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(52,plain,
% 0.56/0.60 ((~![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] : (((C = k1_tsp_2(A, B)) <=> v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | 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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.56/0.60 tff(53,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[52, 46, 45, 44, 43])).
% 0.56/0.60 tff(54,plain,
% 0.56/0.60 (m2_tsp_1(B!1, A!0)),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(55,plain,
% 0.56/0.60 (v2_tsp_2(B!1, A!0)),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(56,plain,
% 0.56/0.60 (~v3_struct_0(B!1)),
% 0.56/0.60 inference(and_elim,[status(thm)],[20])).
% 0.56/0.60 tff(57,plain,
% 0.56/0.60 (((~![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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(58,plain,
% 0.56/0.60 ((~![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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(59,plain,
% 0.56/0.60 ((~![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 = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.56/0.60 tff(60,plain,
% 0.56/0.60 (![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 = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[59, 56, 55, 54, 53])).
% 0.56/0.60 tff(61,plain,
% 0.56/0.60 (^[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))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(62,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[61])).
% 0.56/0.60 tff(63,plain,
% 0.56/0.60 (^[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))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(64,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[63])).
% 0.56/0.60 tff(65,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[64, 62])).
% 0.56/0.61 tff(66,plain,
% 0.56/0.61 (![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)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(67,plain,
% 0.56/0.61 (^[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))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(68,plain,
% 0.56/0.61 (![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)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[67])).
% 0.56/0.61 tff(69,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_tsp_1')).
% 0.56/0.61 tff(70,plain,
% 0.56/0.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.56/0.61 tff(71,plain,
% 0.56/0.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.56/0.61 tff(72,plain,(
% 0.56/0.61 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.56/0.61 inference(skolemize,[status(sab)],[71])).
% 0.56/0.61 tff(73,plain,
% 0.56/0.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.56/0.61 tff(74,plain,
% 0.56/0.61 (((~![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)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(75,plain,
% 0.56/0.61 ((~![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)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(76,plain,
% 0.56/0.61 ((~![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))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.56/0.61 tff(77,plain,
% 0.56/0.61 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[76, 44, 73])).
% 0.56/0.61 tff(78,plain,
% 0.56/0.61 ((~![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))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(79,plain,
% 0.56/0.61 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.56/0.61 tff(80,plain,
% 0.56/0.61 ((~(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)),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(81,plain,
% 0.56/0.61 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[80, 54])).
% 0.56/0.61 tff(82,plain,
% 0.56/0.61 (m1_pre_topc(B!1, A!0)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[81, 79])).
% 0.56/0.61 tff(83,plain,
% 0.56/0.61 (^[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)))))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(84,plain,
% 0.56/0.61 (![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))))))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[83])).
% 0.56/0.61 tff(85,plain,
% 0.56/0.61 (^[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))))))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(86,plain,
% 0.56/0.61 (![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))))))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[85])).
% 0.56/0.61 tff(87,plain,
% 0.56/0.61 (![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))))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(88,plain,
% 0.56/0.61 (^[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))))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(89,plain,
% 0.56/0.61 (![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))))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[88])).
% 0.56/0.61 tff(90,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tsp_2')).
% 0.56/0.61 tff(91,plain,
% 0.56/0.61 (![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))))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.56/0.61 tff(92,plain,
% 0.56/0.61 (![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))))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.56/0.61 tff(93,plain,(
% 0.56/0.61 ![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))))),
% 0.56/0.61 inference(skolemize,[status(sab)],[92])).
% 0.56/0.61 tff(94,plain,
% 0.56/0.61 (![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))))))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.56/0.61 tff(95,plain,
% 0.56/0.61 (![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))))))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.56/0.61 tff(96,plain,
% 0.56/0.61 (((~![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))))))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(97,plain,
% 0.56/0.61 ((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))))))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(98,plain,
% 0.56/0.61 ((~((~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)))))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(99,plain,
% 0.56/0.61 ((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))))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[98])).
% 0.56/0.61 tff(100,plain,
% 0.56/0.61 ((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))))))),
% 0.56/0.61 inference(transitivity,[status(thm)],[99, 97])).
% 0.56/0.61 tff(101,plain,
% 0.56/0.61 (((~![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)))))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[100])).
% 0.56/0.61 tff(102,plain,
% 0.56/0.61 (((~![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))))))),
% 0.56/0.61 inference(transitivity,[status(thm)],[101, 96])).
% 0.56/0.61 tff(103,plain,
% 0.56/0.61 ((~![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))))))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(104,plain,
% 0.56/0.61 ((~![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)))))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.56/0.61 tff(105,plain,
% 0.56/0.61 ((~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)))))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[104, 46, 45, 44, 56, 55, 95])).
% 0.56/0.61 tff(106,plain,
% 0.56/0.61 (~((~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))))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[105, 82])).
% 0.56/0.61 tff(107,plain,
% 0.56/0.61 (((~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))),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(108,plain,
% 0.56/0.61 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.56/0.61 tff(109,plain,
% 0.56/0.61 (((~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)),
% 0.56/0.62 inference(tautology,[status(thm)],[])).
% 0.56/0.62 tff(110,plain,
% 0.56/0.62 (v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.56/0.62 tff(111,plain,
% 0.56/0.62 (((~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))),
% 0.56/0.62 inference(tautology,[status(thm)],[])).
% 0.56/0.62 tff(112,plain,
% 0.56/0.62 (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.56/0.62 tff(113,plain,
% 0.56/0.62 (((~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))),
% 0.56/0.62 inference(tautology,[status(thm)],[])).
% 0.56/0.62 tff(114,plain,
% 0.56/0.62 (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[113, 106])).
% 0.56/0.62 tff(115,plain,
% 0.56/0.62 (((~![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 = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(116,plain,
% 0.56/0.62 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(117,plain,
% 0.56/0.62 (($true <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(118,plain,
% 0.56/0.62 ((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> $true),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(119,plain,
% 0.56/0.62 (((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) <=> ($true <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[118])).
% 0.56/0.62 tff(120,plain,
% 0.56/0.62 (((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.56/0.62 inference(transitivity,[status(thm)],[119, 117])).
% 0.56/0.62 tff(121,plain,
% 0.56/0.62 (((~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) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!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))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[120])).
% 0.56/0.62 tff(122,plain,
% 0.56/0.62 (((~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) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!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))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.56/0.62 inference(transitivity,[status(thm)],[121, 116])).
% 0.56/0.62 tff(123,plain,
% 0.56/0.62 (((~![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 = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | ((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[122])).
% 0.56/0.62 tff(124,plain,
% 0.56/0.62 (((~![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 = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | ((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.56/0.62 inference(transitivity,[status(thm)],[123, 115])).
% 0.56/0.62 tff(125,plain,
% 0.56/0.62 ((~![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 = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | ((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(126,plain,
% 0.56/0.62 ((~![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 = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!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))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.56/0.62 tff(127,plain,
% 0.56/0.62 (v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[126, 114, 112, 110, 108, 60])).
% 0.56/0.62 tff(128,plain,
% 0.56/0.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(129,plain,
% 0.56/0.62 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[128])).
% 0.56/0.62 tff(130,plain,
% 0.56/0.62 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(131,plain,
% 0.56/0.62 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[130])).
% 0.56/0.62 tff(132,plain,
% 0.56/0.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(133,plain,
% 0.56/0.62 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[132])).
% 0.56/0.62 tff(134,plain,
% 0.56/0.62 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.62 inference(transitivity,[status(thm)],[133, 131])).
% 0.56/0.62 tff(135,plain,
% 0.56/0.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, 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)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))) <=> (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))) <=> (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))) <=> ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(136,plain,
% 0.56/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[135])).
% 0.56/0.62 tff(137,plain,
% 0.56/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(138,plain,
% 0.56/0.62 (^[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))))), trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite(((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))) <=> ((~(D = E)) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))), ((m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))) <=> (m1_subset_1(E, u1_struct_0(B)) => ((~(D = E)) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))), rewrite((m1_subset_1(E, u1_struct_0(B)) => ((~(D = E)) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))) <=> ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))), ((m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))) <=> ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))) <=> ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) <=> ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))) <=> ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))), ((v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))) <=> (v3_borsuk_1(C, A, B) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))))), rewrite((v3_borsuk_1(C, A, B) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))) <=> ((~v3_borsuk_1(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))), ((v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))) <=> ((~v3_borsuk_1(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, 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))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((~v3_borsuk_1(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, 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))) => ((~v3_borsuk_1(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))))),
% 0.56/0.63 inference(bind,[status(th)],[])).
% 0.56/0.63 tff(139,plain,
% 0.56/0.63 (![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))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))),
% 0.56/0.63 inference(quant_intro,[status(thm)],[138])).
% 0.56/0.63 tff(140,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))) => (v3_borsuk_1(C, A, B) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ((D = E) => (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l33_tsp_2')).
% 0.56/0.63 tff(141,plain,
% 0.56/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.56/0.63 tff(142,plain,
% 0.56/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.56/0.63 tff(143,plain,(
% 0.56/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)))))),
% 0.56/0.63 inference(skolemize,[status(sab)],[142])).
% 0.56/0.63 tff(144,plain,
% 0.56/0.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.56/0.63 tff(145,plain,
% 0.56/0.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))) | (~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.56/0.63 tff(146,plain,
% 0.56/0.63 (![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[145, 129])).
% 0.56/0.63 tff(147,plain,
% 0.56/0.63 (((~![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))))) <=> ((~![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(148,plain,
% 0.56/0.63 ((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] : ((~v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B)))))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(149,plain,
% 0.56/0.63 (((~![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))))),
% 0.56/0.63 inference(monotonicity,[status(thm)],[148])).
% 0.56/0.63 tff(150,plain,
% 0.56/0.63 (((~![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))))),
% 0.56/0.63 inference(transitivity,[status(thm)],[149, 147])).
% 0.56/0.63 tff(151,plain,
% 0.56/0.63 ((~![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v3_borsuk_1(C, A!0, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(152,plain,
% 0.56/0.63 ((~![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] : ((~v3_borsuk_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A, k1_struct_0(A, D))) | (~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.56/0.63 tff(153,plain,
% 0.56/0.63 (![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[152, 46, 45, 44, 146])).
% 0.56/0.63 tff(154,plain,
% 0.56/0.63 (((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))) | (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)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))) | 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)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(155,plain,
% 0.56/0.63 ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))) | (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)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(156,plain,
% 0.56/0.63 ((~![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))) | 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)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.56/0.63 tff(157,plain,
% 0.56/0.63 (![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[156, 56, 55, 54, 153])).
% 0.56/0.63 tff(158,plain,
% 0.56/0.63 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | ((~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_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | (~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_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(159,plain,
% 0.56/0.64 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))) <=> ((~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_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(160,plain,
% 0.56/0.64 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | ((~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_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.56/0.64 inference(monotonicity,[status(thm)],[159])).
% 0.56/0.64 tff(161,plain,
% 0.56/0.64 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | (~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_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.56/0.64 inference(transitivity,[status(thm)],[160, 158])).
% 0.56/0.64 tff(162,plain,
% 0.56/0.64 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.56/0.64 inference(quant_inst,[status(thm)],[])).
% 0.56/0.64 tff(163,plain,
% 0.56/0.64 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_borsuk_1(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) | (~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_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.56/0.64 tff(164,plain,
% 0.56/0.64 ((~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))),
% 0.56/0.64 inference(unit_resolution,[status(thm)],[163, 114, 112, 110, 108, 157])).
% 0.56/0.64 tff(165,plain,
% 0.56/0.64 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))),
% 0.56/0.64 inference(unit_resolution,[status(thm)],[164, 127])).
% 0.56/0.64 tff(166,plain,
% 0.56/0.64 (m1_subset_1(D!3, u1_struct_0(A!0)) <=> m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.56/0.64 inference(monotonicity,[status(thm)],[23])).
% 0.56/0.64 tff(167,plain,
% 0.56/0.64 (m1_subset_1(C!2, u1_struct_0(A!0)) <=> m1_subset_1(D!3, u1_struct_0(A!0))),
% 0.56/0.64 inference(symmetry,[status(thm)],[166])).
% 0.56/0.64 tff(168,plain,
% 0.56/0.64 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.56/0.64 inference(and_elim,[status(thm)],[20])).
% 0.56/0.64 tff(169,plain,
% 0.56/0.64 (m1_subset_1(D!3, u1_struct_0(A!0))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.56/0.64 tff(170,plain,
% 0.56/0.64 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(171,plain,
% 0.56/0.64 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))))),
% 0.56/0.64 inference(quant_inst,[status(thm)],[])).
% 0.56/0.64 tff(172,plain,
% 0.56/0.64 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~(D = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.56/0.64 tff(173,plain,
% 0.56/0.64 (![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.56/0.64 inference(unit_resolution,[status(thm)],[172, 169, 165])).
% 0.56/0.64 tff(174,plain,
% 0.56/0.64 (m1_subset_1(D!3, u1_struct_0(B!1))),
% 0.56/0.64 inference(or_elim,[status(thm)],[21])).
% 0.56/0.64 tff(175,plain,
% 0.56/0.64 (((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) <=> ((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(176,plain,
% 0.56/0.64 (($false | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))) <=> ((~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(177,plain,
% 0.56/0.64 ((~$true) <=> $false),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(178,plain,
% 0.56/0.64 ((D!3 = D!3) <=> $true),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(179,plain,
% 0.61/0.64 ((~(D!3 = D!3)) <=> (~$true)),
% 0.61/0.64 inference(monotonicity,[status(thm)],[178])).
% 0.61/0.64 tff(180,plain,
% 0.61/0.64 ((~(D!3 = D!3)) <=> $false),
% 0.61/0.64 inference(transitivity,[status(thm)],[179, 177])).
% 0.61/0.64 tff(181,plain,
% 0.61/0.64 (((~(D!3 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))) <=> ($false | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[180])).
% 0.61/0.64 tff(182,plain,
% 0.61/0.64 (((~(D!3 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))) <=> ((~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.61/0.64 inference(transitivity,[status(thm)],[181, 176])).
% 0.61/0.64 tff(183,plain,
% 0.61/0.64 (((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | ((~(D!3 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) <=> ((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[182])).
% 0.61/0.64 tff(184,plain,
% 0.61/0.64 (((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | ((~(D!3 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) <=> ((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.61/0.64 inference(transitivity,[status(thm)],[183, 175])).
% 0.61/0.64 tff(185,plain,
% 0.61/0.64 ((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | ((~(D!3 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(186,plain,
% 0.61/0.64 ((~![E: $i] : ((~(D!3 = E)) | (~m1_subset_1(E, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, E))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))))) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.61/0.64 tff(187,plain,
% 0.61/0.64 (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, D!3))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[186, 174, 173])).
% 0.61/0.64 tff(188,plain,
% 0.61/0.64 (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))),
% 0.61/0.64 inference(transitivity,[status(thm)],[187, 27])).
% 0.61/0.64 tff(189,plain,
% 0.62/0.65 (~(k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D!3))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2)))),
% 0.62/0.65 inference(or_elim,[status(thm)],[21])).
% 0.62/0.65 tff(190,plain,
% 0.62/0.65 ($false),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.62/0.65 % SZS output end Proof
%------------------------------------------------------------------------------