%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP035+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:41 AM UTC 2025
% Result : Theorem 0.20s 0.51s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP035+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:59:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(k6_pre_topc_type, type, (
% 0.20/0.51 k6_pre_topc: ( $i * $i ) > $i)).
% 0.20/0.51 tff(k1_struct_0_type, type, (
% 0.20/0.51 k1_struct_0: ( $i * $i ) > $i)).
% 0.20/0.51 tff(tptp_fun_A_0_type, type, (
% 0.20/0.51 tptp_fun_A_0: $i)).
% 0.20/0.51 tff(k5_pre_topc_type, type, (
% 0.20/0.51 k5_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.51 tff(tptp_fun_B_1_type, type, (
% 0.20/0.51 tptp_fun_B_1: $i)).
% 0.20/0.51 tff(k1_tsp_2_type, type, (
% 0.20/0.51 k1_tsp_2: ( $i * $i ) > $i)).
% 0.20/0.51 tff(m1_subset_1_type, type, (
% 0.20/0.51 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.51 tff(u1_struct_0_type, type, (
% 0.20/0.51 u1_struct_0: $i > $i)).
% 0.20/0.51 tff(v3_borsuk_1_type, type, (
% 0.20/0.51 v3_borsuk_1: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(m2_relset_1_type, type, (
% 0.20/0.51 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(v5_pre_topc_type, type, (
% 0.20/0.51 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(v1_funct_2_type, type, (
% 0.20/0.51 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(v1_funct_1_type, type, (
% 0.20/0.51 v1_funct_1: $i > $o)).
% 0.20/0.51 tff(v2_tsp_2_type, type, (
% 0.20/0.51 v2_tsp_2: ( $i * $i ) > $o)).
% 0.20/0.51 tff(m2_tsp_1_type, type, (
% 0.20/0.51 m2_tsp_1: ( $i * $i ) > $o)).
% 0.20/0.51 tff(v3_struct_0_type, type, (
% 0.20/0.51 v3_struct_0: $i > $o)).
% 0.20/0.51 tff(v2_pre_topc_type, type, (
% 0.20/0.51 v2_pre_topc: $i > $o)).
% 0.20/0.51 tff(l1_pre_topc_type, type, (
% 0.20/0.51 l1_pre_topc: $i > $o)).
% 0.20/0.51 tff(tptp_fun_C_2_type, type, (
% 0.20/0.51 tptp_fun_C_2: $i)).
% 0.20/0.51 tff(m1_pre_topc_type, type, (
% 0.20/0.51 m1_pre_topc: ( $i * $i ) > $o)).
% 0.20/0.51 tff(1,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (^[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))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.51 tff(11,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')).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.51 tff(14,plain,(
% 0.20/0.51 ![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)))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[13])).
% 0.20/0.52 tff(15,plain,
% 0.20/0.52 (![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))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.52 tff(16,plain,
% 0.20/0.52 (![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))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 ((((~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))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 ((((~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))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2)))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 ((((~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))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2)))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 ((((~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))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 ((~![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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = 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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = k6_pre_topc(A, k1_struct_0(A, C)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 ((~![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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = k6_pre_topc(A, k1_struct_0(A, C)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(23,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, 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')).
% 0.20/0.52 tff(24,plain,
% 0.20/0.52 (~![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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = k6_pre_topc(A, k1_struct_0(A, C))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (~![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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = k6_pre_topc(A, k1_struct_0(A, C))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (~![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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = k6_pre_topc(A, k1_struct_0(A, C))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (~![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))) | (~m1_subset_1(C, u1_struct_0(B))) | (k5_pre_topc(A, B, k1_tsp_2(A, B), k6_pre_topc(B, k1_struct_0(B, C))) = k6_pre_topc(A, k1_struct_0(A, C))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 ((~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))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 (l1_pre_topc(A!0)),
% 0.20/0.52 inference(and_elim,[status(thm)],[28])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (v2_pre_topc(A!0)),
% 0.20/0.52 inference(and_elim,[status(thm)],[28])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (~v3_struct_0(A!0)),
% 0.20/0.52 inference(and_elim,[status(thm)],[28])).
% 0.20/0.52 tff(32,plain,
% 0.37/0.52 (((~![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) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = 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) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(33,plain,
% 0.37/0.52 ((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) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(34,plain,
% 0.37/0.52 (((~![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) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))))),
% 0.37/0.52 inference(monotonicity,[status(thm)],[33])).
% 0.37/0.52 tff(35,plain,
% 0.37/0.52 (((~![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) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B)))))),
% 0.37/0.52 inference(transitivity,[status(thm)],[34, 32])).
% 0.37/0.52 tff(36,plain,
% 0.37/0.52 ((~![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))))))),
% 0.37/0.52 inference(quant_inst,[status(thm)],[])).
% 0.37/0.52 tff(37,plain,
% 0.37/0.52 ((~![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) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.37/0.52 tff(38,plain,
% 0.37/0.52 (![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[37, 31, 30, 29, 16])).
% 0.37/0.52 tff(39,plain,
% 0.37/0.52 (m2_tsp_1(B!1, A!0)),
% 0.37/0.52 inference(and_elim,[status(thm)],[28])).
% 0.37/0.52 tff(40,plain,
% 0.37/0.52 (v2_tsp_2(B!1, A!0)),
% 0.37/0.52 inference(and_elim,[status(thm)],[28])).
% 0.37/0.52 tff(41,plain,
% 0.37/0.52 (~v3_struct_0(B!1)),
% 0.37/0.52 inference(and_elim,[status(thm)],[28])).
% 0.37/0.52 tff(42,plain,
% 0.37/0.52 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(43,plain,
% 0.37/0.52 ((v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))) <=> (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(44,plain,
% 0.37/0.52 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))))),
% 0.37/0.52 inference(monotonicity,[status(thm)],[43])).
% 0.37/0.52 tff(45,plain,
% 0.37/0.52 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))),
% 0.37/0.52 inference(transitivity,[status(thm)],[44, 42])).
% 0.37/0.52 tff(46,plain,
% 0.37/0.52 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1))))),
% 0.37/0.52 inference(quant_inst,[status(thm)],[])).
% 0.37/0.52 tff(47,plain,
% 0.37/0.52 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ((C = k1_tsp_2(A!0, B)) <=> v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.37/0.52 tff(48,plain,
% 0.37/0.52 (![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)))),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[47, 41, 40, 39, 38])).
% 0.37/0.52 tff(49,plain,
% 0.37/0.52 (^[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))))),
% 0.37/0.52 inference(bind,[status(th)],[])).
% 0.37/0.52 tff(50,plain,
% 0.37/0.52 (![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)))),
% 0.37/0.52 inference(quant_intro,[status(thm)],[49])).
% 0.37/0.52 tff(51,plain,
% 0.37/0.52 (^[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))))),
% 0.37/0.52 inference(bind,[status(th)],[])).
% 0.37/0.52 tff(52,plain,
% 0.37/0.52 (![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)))),
% 0.37/0.52 inference(quant_intro,[status(thm)],[51])).
% 0.37/0.52 tff(53,plain,
% 0.37/0.52 (![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)))),
% 0.37/0.52 inference(transitivity,[status(thm)],[52, 50])).
% 0.37/0.52 tff(54,plain,
% 0.37/0.52 (![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)))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(55,plain,
% 0.37/0.52 (^[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))))),
% 0.37/0.52 inference(bind,[status(th)],[])).
% 0.37/0.52 tff(56,plain,
% 0.37/0.52 (![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)))),
% 0.37/0.52 inference(quant_intro,[status(thm)],[55])).
% 0.37/0.52 tff(57,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')).
% 0.37/0.52 tff(58,plain,
% 0.37/0.52 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.37/0.52 tff(59,plain,
% 0.37/0.52 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.37/0.52 tff(60,plain,(
% 0.37/0.52 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.37/0.52 inference(skolemize,[status(sab)],[59])).
% 0.37/0.52 tff(61,plain,
% 0.37/0.52 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.37/0.52 tff(62,plain,
% 0.37/0.52 (((~![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)))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(63,plain,
% 0.37/0.52 ((~![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)))),
% 0.37/0.52 inference(quant_inst,[status(thm)],[])).
% 0.37/0.52 tff(64,plain,
% 0.37/0.52 ((~![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))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.37/0.52 tff(65,plain,
% 0.37/0.52 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[64, 29, 61])).
% 0.37/0.52 tff(66,plain,
% 0.37/0.52 ((~![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))),
% 0.37/0.52 inference(quant_inst,[status(thm)],[])).
% 0.37/0.52 tff(67,plain,
% 0.37/0.52 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.37/0.52 tff(68,plain,
% 0.37/0.52 ((~(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)),
% 0.37/0.52 inference(tautology,[status(thm)],[])).
% 0.37/0.52 tff(69,plain,
% 0.37/0.52 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[68, 39])).
% 0.37/0.52 tff(70,plain,
% 0.37/0.52 (m1_pre_topc(B!1, A!0)),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[69, 67])).
% 0.37/0.52 tff(71,plain,
% 0.37/0.52 (^[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)))))))),
% 0.37/0.52 inference(bind,[status(th)],[])).
% 0.37/0.52 tff(72,plain,
% 0.37/0.52 (![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))))))),
% 0.37/0.52 inference(quant_intro,[status(thm)],[71])).
% 0.37/0.52 tff(73,plain,
% 0.37/0.52 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(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))))))))),
% 0.37/0.53 inference(bind,[status(th)],[])).
% 0.37/0.53 tff(74,plain,
% 0.37/0.53 (![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))))))),
% 0.37/0.53 inference(quant_intro,[status(thm)],[73])).
% 0.37/0.53 tff(75,plain,
% 0.37/0.53 (![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))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(76,plain,
% 0.37/0.53 (^[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))))))),
% 0.37/0.53 inference(bind,[status(th)],[])).
% 0.37/0.53 tff(77,plain,
% 0.37/0.53 (![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))))),
% 0.37/0.53 inference(quant_intro,[status(thm)],[76])).
% 0.37/0.53 tff(78,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')).
% 0.37/0.53 tff(79,plain,
% 0.37/0.53 (![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))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.37/0.53 tff(80,plain,
% 0.37/0.53 (![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))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.37/0.53 tff(81,plain,(
% 0.37/0.53 ![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))))),
% 0.37/0.53 inference(skolemize,[status(sab)],[80])).
% 0.37/0.53 tff(82,plain,
% 0.37/0.53 (![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))))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.37/0.53 tff(83,plain,
% 0.37/0.53 (![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))))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.37/0.53 tff(84,plain,
% 0.37/0.53 (((~![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(A!0) | v3_struct_0(B!1) | (~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(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(85,plain,
% 0.37/0.53 ((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(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(86,plain,
% 0.37/0.53 ((~((~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)))))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(87,plain,
% 0.37/0.53 ((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))))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[86])).
% 0.37/0.53 tff(88,plain,
% 0.37/0.53 ((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(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.53 inference(transitivity,[status(thm)],[87, 85])).
% 0.37/0.53 tff(89,plain,
% 0.37/0.53 (((~![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(A!0) | v3_struct_0(B!1) | (~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)))))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[88])).
% 0.37/0.53 tff(90,plain,
% 0.37/0.53 (((~![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(A!0) | v3_struct_0(B!1) | (~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))))))),
% 0.37/0.53 inference(transitivity,[status(thm)],[89, 84])).
% 0.37/0.53 tff(91,plain,
% 0.37/0.53 ((~![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))))))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(92,plain,
% 0.37/0.53 ((~![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(A!0) | v3_struct_0(B!1) | (~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)))))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.37/0.53 tff(93,plain,
% 0.37/0.53 ((~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)))))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[92, 31, 30, 29, 41, 40, 83])).
% 0.37/0.53 tff(94,plain,
% 0.37/0.53 (~((~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))))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[93, 70])).
% 0.37/0.53 tff(95,plain,
% 0.37/0.53 (((~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))),
% 0.37/0.53 inference(tautology,[status(thm)],[])).
% 0.37/0.53 tff(96,plain,
% 0.37/0.53 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.37/0.53 tff(97,plain,
% 0.37/0.53 (((~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)),
% 0.37/0.53 inference(tautology,[status(thm)],[])).
% 0.37/0.53 tff(98,plain,
% 0.37/0.53 (v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.37/0.53 tff(99,plain,
% 0.37/0.53 (((~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))),
% 0.37/0.53 inference(tautology,[status(thm)],[])).
% 0.37/0.53 tff(100,plain,
% 0.37/0.53 (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[99, 94])).
% 0.37/0.53 tff(101,plain,
% 0.37/0.53 (((~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))),
% 0.37/0.53 inference(tautology,[status(thm)],[])).
% 0.37/0.53 tff(102,plain,
% 0.37/0.53 (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[101, 94])).
% 0.37/0.53 tff(103,plain,
% 0.37/0.53 (((~![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: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ((C = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(C, A!0, B!1)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(104,plain,
% 0.38/0.54 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(105,plain,
% 0.38/0.54 (($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)),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(106,plain,
% 0.38/0.54 ((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> $true),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(107,plain,
% 0.38/0.54 (((k1_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)) <=> ($true <=> v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[106])).
% 0.38/0.54 tff(108,plain,
% 0.38/0.54 (((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)),
% 0.38/0.54 inference(transitivity,[status(thm)],[107, 105])).
% 0.38/0.54 tff(109,plain,
% 0.38/0.54 (((~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))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[108])).
% 0.38/0.54 tff(110,plain,
% 0.38/0.54 (((~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))),
% 0.38/0.54 inference(transitivity,[status(thm)],[109, 104])).
% 0.38/0.54 tff(111,plain,
% 0.38/0.54 (((~![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)))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[110])).
% 0.38/0.54 tff(112,plain,
% 0.38/0.54 (((~![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))),
% 0.38/0.54 inference(transitivity,[status(thm)],[111, 103])).
% 0.38/0.54 tff(113,plain,
% 0.38/0.54 ((~![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)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(114,plain,
% 0.38/0.54 ((~![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)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.38/0.54 tff(115,plain,
% 0.38/0.54 (v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[114, 102, 100, 98, 96, 48])).
% 0.38/0.54 tff(116,plain,
% 0.38/0.54 (^[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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(117,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[116])).
% 0.38/0.54 tff(118,plain,
% 0.38/0.54 (^[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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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)))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(119,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[118])).
% 0.38/0.54 tff(120,plain,
% 0.38/0.54 (^[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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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)))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(121,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[120])).
% 0.38/0.54 tff(122,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[121, 119])).
% 0.38/0.54 tff(123,plain,
% 0.38/0.54 (^[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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B))) <=> (![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B))) <=> (![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B))) <=> ![C: $i] : (![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(124,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[123])).
% 0.38/0.54 tff(125,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B)))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(126,plain,
% 0.38/0.54 (^[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(trans(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)))))), trans(der(![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)))) <=> ![E: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))), elim_unused(![E: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))), (![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(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))), ((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)) => ((~m1_subset_1(D, u1_struct_0(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(D, u1_struct_0(B))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))), ((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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))))), (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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] : (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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))))), rewrite((v3_borsuk_1(C, A, B) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D))))) <=> ((~v3_borsuk_1(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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] : (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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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] : (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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))), 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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B)))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(127,plain,
% 0.38/0.54 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B)))))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[126])).
% 0.38/0.55 tff(128,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')).
% 0.38/0.55 tff(129,plain,
% 0.38/0.55 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B)))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.38/0.55 tff(130,plain,
% 0.38/0.55 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B)))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.38/0.55 tff(131,plain,(
% 0.38/0.55 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~v3_borsuk_1(C, A, B)))))),
% 0.38/0.55 inference(skolemize,[status(sab)],[130])).
% 0.38/0.55 tff(132,plain,
% 0.38/0.55 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.38/0.55 tff(133,plain,
% 0.38/0.55 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))) | (~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))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.38/0.55 tff(134,plain,
% 0.38/0.55 (![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[133, 117])).
% 0.38/0.55 tff(135,plain,
% 0.38/0.55 (((~![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~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] : ((~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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B)))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(136,plain,
% 0.38/0.55 ((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(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B)))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(137,plain,
% 0.38/0.55 (((~![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | (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(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[136])).
% 0.38/0.55 tff(138,plain,
% 0.38/0.55 (((~![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | (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(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = 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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B)))))),
% 0.38/0.55 inference(transitivity,[status(thm)],[137, 135])).
% 0.38/0.55 tff(139,plain,
% 0.38/0.55 ((~![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | (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(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(140,plain,
% 0.38/0.55 ((~![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(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (k5_pre_topc(A, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A, k1_struct_0(A, D)))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.38/0.55 tff(141,plain,
% 0.38/0.55 (![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[140, 31, 30, 29, 134])).
% 0.38/0.55 tff(142,plain,
% 0.38/0.55 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(143,plain,
% 0.38/0.55 ((v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v3_borsuk_1(C, A!0, B!1)))) <=> (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(144,plain,
% 0.38/0.55 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v3_borsuk_1(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[143])).
% 0.38/0.55 tff(145,plain,
% 0.38/0.55 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v3_borsuk_1(C, A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))))),
% 0.38/0.55 inference(transitivity,[status(thm)],[144, 142])).
% 0.38/0.55 tff(146,plain,
% 0.38/0.55 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v3_borsuk_1(C, A!0, B!1))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(147,plain,
% 0.38/0.55 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, C, k6_pre_topc(B, k1_struct_0(B, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v3_borsuk_1(C, A!0, B))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.38/0.55 tff(148,plain,
% 0.38/0.55 (![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[147, 41, 40, 39, 141])).
% 0.38/0.56 tff(149,plain,
% 0.38/0.56 (((~![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))) <=> ((~![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(150,plain,
% 0.38/0.56 (((~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))) | (~m1_subset_1(D, 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))) = 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(151,plain,
% 0.38/0.56 (((~![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | (~m1_subset_1(D, 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))) = 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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[150])).
% 0.38/0.56 tff(152,plain,
% 0.38/0.56 (((~![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | (~m1_subset_1(D, 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))) = 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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[151, 149])).
% 0.38/0.56 tff(153,plain,
% 0.38/0.56 ((~![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(154,plain,
% 0.38/0.56 ((~![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))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, C, k6_pre_topc(B!1, k1_struct_0(B!1, D))) = 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))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.38/0.57 tff(155,plain,
% 0.38/0.57 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D)))) | (~v3_borsuk_1(k1_tsp_2(A!0, B!1), A!0, B!1))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[154, 102, 100, 98, 96, 148])).
% 0.38/0.57 tff(156,plain,
% 0.38/0.57 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[155, 115])).
% 0.38/0.57 tff(157,plain,
% 0.38/0.57 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))),
% 0.38/0.57 inference(and_elim,[status(thm)],[28])).
% 0.38/0.57 tff(158,plain,
% 0.38/0.57 (~(k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2)))),
% 0.38/0.57 inference(or_elim,[status(thm)],[157])).
% 0.38/0.57 tff(159,plain,
% 0.38/0.57 (m1_subset_1(C!2, u1_struct_0(B!1))),
% 0.38/0.57 inference(or_elim,[status(thm)],[157])).
% 0.38/0.57 tff(160,plain,
% 0.38/0.57 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.38/0.57 inference(or_elim,[status(thm)],[157])).
% 0.38/0.57 tff(161,plain,
% 0.38/0.57 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(162,plain,
% 0.38/0.57 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, 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))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, 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, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(163,plain,
% 0.38/0.57 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, D))) = k6_pre_topc(A!0, k1_struct_0(A!0, D))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k6_pre_topc(B!1, k1_struct_0(B!1, C!2))) = k6_pre_topc(A!0, k1_struct_0(A!0, C!2)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.38/0.57 tff(164,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[163, 160, 159, 158, 156])).
% 0.38/0.57 % SZS output end Proof
% 0.38/0.57 % E exiting
%------------------------------------------------------------------------------