%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP033+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:42:40 AM UTC 2025
% Result : Theorem 4.78s 5.00s
% Output : Proof 4.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP033+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:57:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.78/5.00 % SZS status Theorem
% 4.78/5.00 % SZS output start Proof
% 4.78/5.00 tff(k1_struct_0_type, type, (
% 4.78/5.00 k1_struct_0: ( $i * $i ) > $i)).
% 4.78/5.00 tff(k8_funct_2_type, type, (
% 4.78/5.00 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 4.78/5.00 tff(tptp_fun_E_25_type, type, (
% 4.78/5.00 tptp_fun_E_25: ( $i * $i * $i ) > $i)).
% 4.78/5.00 tff(tptp_fun_A_0_type, type, (
% 4.78/5.00 tptp_fun_A_0: $i)).
% 4.78/5.00 tff(tptp_fun_B_1_type, type, (
% 4.78/5.00 tptp_fun_B_1: $i)).
% 4.78/5.00 tff(tptp_fun_C_2_type, type, (
% 4.78/5.00 tptp_fun_C_2: $i)).
% 4.78/5.00 tff(u1_struct_0_type, type, (
% 4.78/5.00 u1_struct_0: $i > $i)).
% 4.78/5.00 tff(k5_subset_1_type, type, (
% 4.78/5.00 k5_subset_1: ( $i * $i * $i ) > $i)).
% 4.78/5.00 tff(k4_tex_4_type, type, (
% 4.78/5.00 k4_tex_4: ( $i * $i ) > $i)).
% 4.78/5.00 tff(k1_tarski_type, type, (
% 4.78/5.00 k1_tarski: $i > $i)).
% 4.78/5.00 tff(m1_subset_1_type, type, (
% 4.78/5.00 m1_subset_1: ( $i * $i ) > $o)).
% 4.78/5.00 tff(k1_zfmisc_1_type, type, (
% 4.78/5.00 k1_zfmisc_1: $i > $i)).
% 4.78/5.00 tff(m1_pre_topc_type, type, (
% 4.78/5.00 m1_pre_topc: ( $i * $i ) > $o)).
% 4.78/5.00 tff(m2_tsp_1_type, type, (
% 4.78/5.00 m2_tsp_1: ( $i * $i ) > $o)).
% 4.78/5.00 tff(l1_pre_topc_type, type, (
% 4.78/5.00 l1_pre_topc: $i > $o)).
% 4.78/5.00 tff(m2_relset_1_type, type, (
% 4.78/5.00 m2_relset_1: ( $i * $i * $i ) > $o)).
% 4.78/5.00 tff(v5_pre_topc_type, type, (
% 4.78/5.00 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 4.78/5.00 tff(v1_funct_2_type, type, (
% 4.78/5.00 v1_funct_2: ( $i * $i * $i ) > $o)).
% 4.78/5.00 tff(v1_funct_1_type, type, (
% 4.78/5.00 v1_funct_1: $i > $o)).
% 4.78/5.00 tff(r2_hidden_type, type, (
% 4.78/5.00 r2_hidden: ( $i * $i ) > $o)).
% 4.78/5.00 tff(v3_borsuk_1_type, type, (
% 4.78/5.00 v3_borsuk_1: ( $i * $i * $i ) > $o)).
% 4.78/5.00 tff(v2_tsp_2_type, type, (
% 4.78/5.00 v2_tsp_2: ( $i * $i ) > $o)).
% 4.78/5.00 tff(v3_struct_0_type, type, (
% 4.78/5.00 v3_struct_0: $i > $o)).
% 4.78/5.00 tff(v2_pre_topc_type, type, (
% 4.78/5.00 v2_pre_topc: $i > $o)).
% 4.78/5.00 tff(m1_relset_1_type, type, (
% 4.78/5.00 m1_relset_1: ( $i * $i * $i ) > $o)).
% 4.78/5.00 tff(v1_xboole_0_type, type, (
% 4.78/5.00 v1_xboole_0: $i > $o)).
% 4.78/5.00 tff(l1_struct_0_type, type, (
% 4.78/5.00 l1_struct_0: $i > $o)).
% 4.78/5.00 tff(k1_funct_1_type, type, (
% 4.78/5.00 k1_funct_1: ( $i * $i ) > $i)).
% 4.78/5.00 tff(r1_tarski_type, type, (
% 4.78/5.00 r1_tarski: ( $i * $i ) > $o)).
% 4.78/5.00 tff(tptp_fun_C_4_type, type, (
% 4.78/5.00 tptp_fun_C_4: ( $i * $i ) > $i)).
% 4.78/5.00 tff(v1_tsp_1_type, type, (
% 4.78/5.00 v1_tsp_1: ( $i * $i ) > $o)).
% 4.78/5.00 tff(tptp_fun_C_3_type, type, (
% 4.78/5.00 tptp_fun_C_3: ( $i * $i ) > $i)).
% 4.78/5.00 tff(v1_tsp_2_type, type, (
% 4.78/5.00 v1_tsp_2: ( $i * $i ) > $o)).
% 4.78/5.00 tff(tptp_fun_C_5_type, type, (
% 4.78/5.00 tptp_fun_C_5: ( $i * $i ) > $i)).
% 4.78/5.00 tff(k2_tex_4_type, type, (
% 4.78/5.00 k2_tex_4: ( $i * $i ) > $i)).
% 4.78/5.00 tff(1,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(2,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[1])).
% 4.78/5.00 tff(3,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(4,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[3])).
% 4.78/5.00 tff(5,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[4, 2])).
% 4.78/5.00 tff(6,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(7,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(8,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[7])).
% 4.78/5.00 tff(9,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_tsp_1')).
% 4.78/5.01 tff(10,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[9, 8])).
% 4.78/5.01 tff(11,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[10, 6])).
% 4.78/5.01 tff(12,plain,(
% 4.78/5.01 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.78/5.01 inference(skolemize,[status(sab)],[11])).
% 4.78/5.01 tff(13,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[12, 5])).
% 4.78/5.01 tff(14,plain,
% 4.78/5.01 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(15,plain,
% 4.78/5.01 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(16,plain,
% 4.78/5.01 (((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(17,plain,
% 4.78/5.01 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.78/5.01 inference(monotonicity,[status(thm)],[16])).
% 4.78/5.01 tff(18,plain,
% 4.78/5.01 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.78/5.01 inference(transitivity,[status(thm)],[17, 15])).
% 4.78/5.01 tff(19,plain,
% 4.78/5.01 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.78/5.01 inference(monotonicity,[status(thm)],[18])).
% 4.78/5.01 tff(20,plain,
% 4.78/5.01 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & ((~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.78/5.01 inference(transitivity,[status(thm)],[19, 14])).
% 4.78/5.01 tff(21,plain,
% 4.78/5.01 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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))))))))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(22,plain,
% 4.78/5.01 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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))))))))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 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] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(A, D))) => v3_borsuk_1(C, A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_tsp_2')).
% 4.78/5.01 tff(24,plain,
% 4.78/5.01 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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)))))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[23, 22])).
% 4.78/5.01 tff(25,plain,
% 4.78/5.01 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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)))))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[24, 21])).
% 4.78/5.01 tff(26,plain,
% 4.78/5.01 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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)))))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[25, 21])).
% 4.78/5.01 tff(27,plain,
% 4.78/5.01 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | r2_hidden(k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, D), k4_tex_4(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)))))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[26, 21])).
% 4.78/5.01 tff(28,plain,
% 4.78/5.01 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~v3_borsuk_1(C!2, A!0, B!1)) & ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v5_pre_topc(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[27, 20])).
% 4.78/5.01 tff(29,plain,
% 4.78/5.01 (l1_pre_topc(A!0)),
% 4.78/5.01 inference(and_elim,[status(thm)],[28])).
% 4.78/5.01 tff(30,plain,
% 4.78/5.01 (((~![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)))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(31,plain,
% 4.78/5.01 ((~![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)))),
% 4.78/5.01 inference(quant_inst,[status(thm)],[])).
% 4.78/5.01 tff(32,plain,
% 4.78/5.01 ((~![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))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[31, 30])).
% 4.78/5.01 tff(33,plain,
% 4.78/5.01 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[32, 29, 13])).
% 4.78/5.01 tff(34,plain,
% 4.78/5.01 ((~![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))),
% 4.78/5.01 inference(quant_inst,[status(thm)],[])).
% 4.78/5.01 tff(35,plain,
% 4.78/5.01 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[34, 33])).
% 4.78/5.01 tff(36,plain,
% 4.78/5.01 (m2_tsp_1(B!1, A!0)),
% 4.78/5.01 inference(and_elim,[status(thm)],[28])).
% 4.78/5.01 tff(37,plain,
% 4.78/5.01 ((~(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)),
% 4.78/5.01 inference(tautology,[status(thm)],[])).
% 4.78/5.01 tff(38,plain,
% 4.78/5.01 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[37, 36])).
% 4.78/5.01 tff(39,plain,
% 4.78/5.01 (m1_pre_topc(B!1, A!0)),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[38, 35])).
% 4.78/5.01 tff(40,plain,
% 4.78/5.01 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.78/5.01 inference(bind,[status(th)],[])).
% 4.78/5.01 tff(41,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(quant_intro,[status(thm)],[40])).
% 4.78/5.01 tff(42,plain,
% 4.78/5.01 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.78/5.01 inference(bind,[status(th)],[])).
% 4.78/5.01 tff(43,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(quant_intro,[status(thm)],[42])).
% 4.78/5.01 tff(44,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(transitivity,[status(thm)],[43, 41])).
% 4.78/5.01 tff(45,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(46,plain,
% 4.78/5.01 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 4.78/5.01 inference(bind,[status(th)],[])).
% 4.78/5.01 tff(47,plain,
% 4.78/5.01 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(quant_intro,[status(thm)],[46])).
% 4.78/5.01 tff(48,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_tsep_1')).
% 4.78/5.01 tff(49,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[48, 47])).
% 4.78/5.01 tff(50,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[49, 45])).
% 4.78/5.01 tff(51,plain,(
% 4.78/5.01 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(skolemize,[status(sab)],[50])).
% 4.78/5.01 tff(52,plain,
% 4.78/5.01 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[51, 44])).
% 4.78/5.01 tff(53,plain,
% 4.78/5.01 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(54,plain,
% 4.78/5.01 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.78/5.01 inference(quant_inst,[status(thm)],[])).
% 4.78/5.01 tff(55,plain,
% 4.78/5.01 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[54, 53])).
% 4.78/5.01 tff(56,plain,
% 4.78/5.01 (![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[55, 29, 52])).
% 4.78/5.01 tff(57,plain,
% 4.78/5.01 (((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(58,plain,
% 4.78/5.01 ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.78/5.01 inference(quant_inst,[status(thm)],[])).
% 4.78/5.01 tff(59,plain,
% 4.78/5.01 ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[58, 57])).
% 4.78/5.01 tff(60,plain,
% 4.78/5.01 ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[59, 56])).
% 4.78/5.01 tff(61,plain,
% 4.78/5.01 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[60, 39])).
% 4.78/5.01 tff(62,plain,
% 4.78/5.01 (^[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] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 4.78/5.01 inference(bind,[status(th)],[])).
% 4.78/5.01 tff(63,plain,
% 4.78/5.01 (![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.78/5.01 inference(quant_intro,[status(thm)],[62])).
% 4.78/5.01 tff(64,plain,
% 4.78/5.01 (^[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] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 4.78/5.01 inference(bind,[status(th)],[])).
% 4.78/5.01 tff(65,plain,
% 4.78/5.01 (![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.78/5.01 inference(quant_intro,[status(thm)],[64])).
% 4.78/5.01 tff(66,plain,
% 4.78/5.01 (![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.78/5.01 inference(transitivity,[status(thm)],[65, 63])).
% 4.78/5.01 tff(67,plain,
% 4.78/5.01 (^[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)))))), ((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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))) <=> (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))))), rewrite((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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))) <=> (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))) <=> (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (![C: $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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))) <=> ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~((~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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, 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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), 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] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 4.78/5.01 inference(bind,[status(th)],[])).
% 4.78/5.01 tff(68,plain,
% 4.78/5.01 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.78/5.01 inference(quant_intro,[status(thm)],[67])).
% 4.78/5.01 tff(69,plain,
% 4.78/5.01 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))),
% 4.78/5.01 inference(rewrite,[status(thm)],[])).
% 4.78/5.01 tff(70,plain,
% 4.78/5.01 (^[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(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) <=> ((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))), ((((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)) <=> (((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))), rewrite((((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)) <=> ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B))), ((((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)) <=> ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B)))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B))))), rewrite((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | v3_borsuk_1(C, A, B))) <=> (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))), ((m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> ![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), trans(trans(der(![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) <=> ![D: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))), elim_unused(![D: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))), (![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), trans(monotonicity(rewrite((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) <=> (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))), (((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), rewrite(((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) <=> (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))), (((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | v3_borsuk_1(C, A, B) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) <=> (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), (![D: $i] : (v3_borsuk_1(C, A, B) | (~((D = u1_struct_0(B)) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), (![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))) <=> (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => 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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))), 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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))) <=> (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, 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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B)))) <=> ![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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))) <=> (((~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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))), rewrite((((~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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))) <=> ((~((~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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))) <=> ((~((~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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))) <=> ![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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => 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] : (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))))), 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] : (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E)))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => 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] : (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))))),
% 4.78/5.02 inference(bind,[status(th)],[])).
% 4.78/5.02 tff(71,plain,
% 4.78/5.02 (![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, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => 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] : (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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))),
% 4.78/5.02 inference(quant_intro,[status(thm)],[70])).
% 4.78/5.02 tff(72,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))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (((D = u1_struct_0(B)) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => (k5_subset_1(u1_struct_0(A), D, k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))) => v3_borsuk_1(C, A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_tsp_2')).
% 4.78/5.02 tff(73,plain,
% 4.78/5.02 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))),
% 4.78/5.02 inference(modus_ponens,[status(thm)],[72, 71])).
% 4.78/5.02 tff(74,plain,
% 4.78/5.02 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, E)) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))))))))),
% 4.78/5.02 inference(modus_ponens,[status(thm)],[73, 69])).
% 4.78/5.02 tff(75,plain,(
% 4.78/5.02 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : (v3_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)))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))))))),
% 4.78/5.02 inference(skolemize,[status(sab)],[74])).
% 4.78/5.02 tff(76,plain,
% 4.78/5.02 (![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.78/5.02 inference(modus_ponens,[status(thm)],[75, 68])).
% 4.78/5.02 tff(77,plain,
% 4.78/5.02 (![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.78/5.02 inference(modus_ponens,[status(thm)],[76, 66])).
% 4.78/5.02 tff(78,plain,
% 4.78/5.02 (v2_pre_topc(A!0)),
% 4.78/5.02 inference(and_elim,[status(thm)],[28])).
% 4.78/5.02 tff(79,plain,
% 4.78/5.02 (~v3_struct_0(A!0)),
% 4.78/5.02 inference(and_elim,[status(thm)],[28])).
% 4.78/5.02 tff(80,plain,
% 4.78/5.02 (((~![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | 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] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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))))))),
% 4.78/5.02 inference(rewrite,[status(thm)],[])).
% 4.78/5.02 tff(81,plain,
% 4.78/5.02 ((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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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))))))),
% 4.78/5.02 inference(rewrite,[status(thm)],[])).
% 4.78/5.02 tff(82,plain,
% 4.78/5.02 (((~![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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)))))))),
% 4.78/5.02 inference(monotonicity,[status(thm)],[81])).
% 4.78/5.02 tff(83,plain,
% 4.78/5.02 (((~![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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] : (v3_borsuk_1(C, A, B) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | 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] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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))))))),
% 4.78/5.02 inference(transitivity,[status(thm)],[82, 80])).
% 4.78/5.02 tff(84,plain,
% 4.78/5.02 ((~![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | (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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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))))))),
% 4.78/5.02 inference(quant_inst,[status(thm)],[])).
% 4.78/5.02 tff(85,plain,
% 4.78/5.02 ((~![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) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A), u1_struct_0(A))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k4_tex_4(A, tptp_fun_E_25(C, B, A))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), C, tptp_fun_E_25(C, B, A)))))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) | 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] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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)))))),
% 4.87/5.02 inference(modus_ponens,[status(thm)],[84, 83])).
% 4.87/5.02 tff(86,plain,
% 4.87/5.02 (![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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)))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[85, 79, 78, 29, 77])).
% 4.87/5.02 tff(87,plain,
% 4.87/5.02 (v2_tsp_2(B!1, A!0)),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(88,plain,
% 4.87/5.02 (~v3_struct_0(B!1)),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(89,plain,
% 4.87/5.02 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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)))))),
% 4.87/5.02 inference(rewrite,[status(thm)],[])).
% 4.87/5.02 tff(90,plain,
% 4.87/5.02 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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)))))),
% 4.87/5.02 inference(quant_inst,[status(thm)],[])).
% 4.87/5.02 tff(91,plain,
% 4.87/5.02 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k4_tex_4(A!0, tptp_fun_E_25(C, B, A!0))) = k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), C, tptp_fun_E_25(C, B, A!0)))))) | (~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(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))),
% 4.87/5.02 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.87/5.02 tff(92,plain,
% 4.87/5.02 (![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))),
% 4.87/5.02 inference(unit_resolution,[status(thm)],[91, 88, 87, 36, 86])).
% 4.87/5.02 tff(93,plain,
% 4.87/5.02 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(94,plain,
% 4.87/5.02 (v5_pre_topc(C!2, A!0, B!1)),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(95,plain,
% 4.87/5.02 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(96,plain,
% 4.87/5.02 (v1_funct_1(C!2)),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(97,plain,
% 4.87/5.02 (~v3_borsuk_1(C!2, A!0, B!1)),
% 4.87/5.02 inference(and_elim,[status(thm)],[28])).
% 4.87/5.02 tff(98,plain,
% 4.87/5.02 (((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_1(C!2)) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)))) <=> ((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | v3_borsuk_1(C!2, A!0, B!1) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_1(C!2)) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)))),
% 4.87/5.02 inference(rewrite,[status(thm)],[])).
% 4.87/5.02 tff(99,plain,
% 4.87/5.02 ((v3_borsuk_1(C!2, A!0, B!1) | (~v1_funct_1(C!2)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> (v3_borsuk_1(C!2, A!0, B!1) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_1(C!2)) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)))),
% 4.87/5.02 inference(rewrite,[status(thm)],[])).
% 4.87/5.02 tff(100,plain,
% 4.87/5.02 (((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~v1_funct_1(C!2)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_1(C!2)) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[99])).
% 4.87/5.03 tff(101,plain,
% 4.87/5.03 (((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~v1_funct_1(C!2)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | v3_borsuk_1(C!2, A!0, B!1) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_1(C!2)) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)))),
% 4.87/5.03 inference(transitivity,[status(thm)],[100, 98])).
% 4.87/5.03 tff(102,plain,
% 4.87/5.03 ((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | (v3_borsuk_1(C!2, A!0, B!1) | (~v1_funct_1(C!2)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(103,plain,
% 4.87/5.03 ((~![C: $i] : (v3_borsuk_1(C, A!0, B!1) | (~v1_funct_1(C)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~m1_subset_1(tptp_fun_E_25(C, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C, tptp_fun_E_25(C, B!1, A!0)))))) | (~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))))) | v3_borsuk_1(C!2, A!0, B!1) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_1(C!2)) | (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C!2, A!0, B!1))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[102, 101])).
% 4.87/5.03 tff(104,plain,
% 4.87/5.03 (~((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[103, 97, 96, 95, 94, 93, 92, 61])).
% 4.87/5.03 tff(105,plain,
% 4.87/5.03 (((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))))) | m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))),
% 4.87/5.03 inference(tautology,[status(thm)],[])).
% 4.87/5.03 tff(106,plain,
% 4.87/5.03 (m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[105, 104])).
% 4.87/5.03 tff(107,plain,
% 4.87/5.03 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(108,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[107])).
% 4.87/5.03 tff(109,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(110,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 4.87/5.03 tff(111,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[110, 109])).
% 4.87/5.03 tff(112,plain,(
% 4.87/5.03 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.87/5.03 inference(skolemize,[status(sab)],[111])).
% 4.87/5.03 tff(113,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[112, 108])).
% 4.87/5.03 tff(114,plain,
% 4.87/5.03 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(115,plain,
% 4.87/5.03 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[114, 113])).
% 4.87/5.03 tff(116,plain,
% 4.87/5.03 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.87/5.03 inference(tautology,[status(thm)],[])).
% 4.87/5.03 tff(117,plain,
% 4.87/5.03 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[116, 93])).
% 4.87/5.03 tff(118,plain,
% 4.87/5.03 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[117, 115])).
% 4.87/5.03 tff(119,plain,
% 4.87/5.03 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(120,plain,
% 4.87/5.03 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[119])).
% 4.87/5.03 tff(121,plain,
% 4.87/5.03 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(122,plain,
% 4.87/5.03 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(123,plain,
% 4.87/5.03 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[122])).
% 4.87/5.03 tff(124,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 4.87/5.03 tff(125,plain,
% 4.87/5.03 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.87/5.03 tff(126,plain,
% 4.87/5.03 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[125, 121])).
% 4.87/5.03 tff(127,plain,(
% 4.87/5.03 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(skolemize,[status(sab)],[126])).
% 4.87/5.03 tff(128,plain,
% 4.87/5.03 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[127, 120])).
% 4.87/5.03 tff(129,plain,
% 4.87/5.03 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(130,plain,
% 4.87/5.03 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(131,plain,
% 4.87/5.03 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[130, 129])).
% 4.87/5.03 tff(132,plain,
% 4.87/5.03 (l1_struct_0(A!0)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[131, 29, 128])).
% 4.87/5.03 tff(133,plain,
% 4.87/5.03 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(134,plain,
% 4.87/5.03 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[133])).
% 4.87/5.03 tff(135,plain,
% 4.87/5.03 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(136,plain,
% 4.87/5.03 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[135])).
% 4.87/5.03 tff(137,plain,
% 4.87/5.03 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(138,plain,
% 4.87/5.03 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(139,plain,
% 4.87/5.03 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[138])).
% 4.87/5.03 tff(140,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 4.87/5.03 tff(141,plain,
% 4.87/5.03 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[140, 139])).
% 4.87/5.03 tff(142,plain,
% 4.87/5.03 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[141, 137])).
% 4.87/5.03 tff(143,plain,(
% 4.87/5.03 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.87/5.03 inference(skolemize,[status(sab)],[142])).
% 4.87/5.03 tff(144,plain,
% 4.87/5.03 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[143, 136])).
% 4.87/5.03 tff(145,plain,
% 4.87/5.03 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[144, 134])).
% 4.87/5.03 tff(146,plain,
% 4.87/5.03 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(147,plain,
% 4.87/5.03 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(148,plain,
% 4.87/5.03 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[147])).
% 4.87/5.03 tff(149,plain,
% 4.87/5.03 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 4.87/5.03 inference(transitivity,[status(thm)],[148, 146])).
% 4.87/5.03 tff(150,plain,
% 4.87/5.03 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(151,plain,
% 4.87/5.03 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[150, 149])).
% 4.87/5.03 tff(152,plain,
% 4.87/5.03 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[151, 79, 145])).
% 4.87/5.03 tff(153,plain,
% 4.87/5.03 (~v1_xboole_0(u1_struct_0(A!0))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[152, 132])).
% 4.87/5.03 tff(154,plain,
% 4.87/5.03 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(155,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[154])).
% 4.87/5.03 tff(156,plain,
% 4.87/5.03 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(157,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[156])).
% 4.87/5.03 tff(158,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(159,plain,
% 4.87/5.03 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(160,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[159])).
% 4.87/5.03 tff(161,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => m1_subset_1(k8_funct_2(A, B, C, D), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k8_funct_2')).
% 4.87/5.03 tff(162,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[161, 160])).
% 4.87/5.03 tff(163,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[162, 158])).
% 4.87/5.03 tff(164,plain,(
% 4.87/5.03 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | m1_subset_1(k8_funct_2(A, B, C, D), B))),
% 4.87/5.03 inference(skolemize,[status(sab)],[163])).
% 4.87/5.03 tff(165,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[164, 157])).
% 4.87/5.03 tff(166,plain,
% 4.87/5.03 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[165, 155])).
% 4.87/5.03 tff(167,plain,
% 4.87/5.03 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(168,plain,
% 4.87/5.03 ((m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(169,plain,
% 4.87/5.03 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))))),
% 4.87/5.03 inference(monotonicity,[status(thm)],[168])).
% 4.87/5.03 tff(170,plain,
% 4.87/5.03 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 4.87/5.03 inference(transitivity,[status(thm)],[169, 167])).
% 4.87/5.03 tff(171,plain,
% 4.87/5.03 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(172,plain,
% 4.87/5.03 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k8_funct_2(A, B, C, D), B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[171, 170])).
% 4.87/5.03 tff(173,plain,
% 4.87/5.03 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[172, 96, 95, 166, 153, 118, 106])).
% 4.87/5.03 tff(174,plain,
% 4.87/5.03 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(175,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[174])).
% 4.87/5.03 tff(176,plain,
% 4.87/5.03 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(177,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[176])).
% 4.87/5.03 tff(178,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(transitivity,[status(thm)],[177, 175])).
% 4.87/5.03 tff(179,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(180,plain,
% 4.87/5.03 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m2_tsp_1(B, A) => l1_pre_topc(B)) <=> (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), (![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)) <=> ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), ((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))), rewrite((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), ((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(181,plain,
% 4.87/5.03 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[180])).
% 4.87/5.03 tff(182,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_tsp_1')).
% 4.87/5.03 tff(183,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[182, 181])).
% 4.87/5.03 tff(184,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[183, 179])).
% 4.87/5.03 tff(185,plain,(
% 4.87/5.03 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(skolemize,[status(sab)],[184])).
% 4.87/5.03 tff(186,plain,
% 4.87/5.03 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[185, 178])).
% 4.87/5.03 tff(187,plain,
% 4.87/5.03 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | (~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(188,plain,
% 4.87/5.03 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(189,plain,
% 4.87/5.03 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | (~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[188, 187])).
% 4.87/5.03 tff(190,plain,
% 4.87/5.03 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[189, 29, 186])).
% 4.87/5.03 tff(191,plain,
% 4.87/5.03 (((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))) <=> ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(192,plain,
% 4.87/5.03 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(193,plain,
% 4.87/5.03 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[192, 191])).
% 4.87/5.03 tff(194,plain,
% 4.87/5.03 (l1_pre_topc(B!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[193, 36, 190])).
% 4.87/5.03 tff(195,plain,
% 4.87/5.03 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(196,plain,
% 4.87/5.03 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 4.87/5.03 inference(quant_inst,[status(thm)],[])).
% 4.87/5.03 tff(197,plain,
% 4.87/5.03 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[196, 195])).
% 4.87/5.03 tff(198,plain,
% 4.87/5.03 (l1_struct_0(B!1)),
% 4.87/5.03 inference(unit_resolution,[status(thm)],[197, 128, 194])).
% 4.87/5.03 tff(199,plain,
% 4.87/5.03 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(200,plain,
% 4.87/5.03 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[199])).
% 4.87/5.03 tff(201,plain,
% 4.87/5.03 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> ((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))))), rewrite(((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(202,plain,
% 4.87/5.03 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[201])).
% 4.87/5.03 tff(203,plain,
% 4.87/5.03 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 4.87/5.03 inference(rewrite,[status(thm)],[])).
% 4.87/5.03 tff(204,plain,
% 4.87/5.03 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))))),
% 4.87/5.03 inference(bind,[status(th)],[])).
% 4.87/5.03 tff(205,plain,
% 4.87/5.03 (![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 4.87/5.03 inference(quant_intro,[status(thm)],[204])).
% 4.87/5.03 tff(206,axiom,(![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) => (k1_struct_0(A, B) = k1_tarski(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_struct_0')).
% 4.87/5.03 tff(207,plain,
% 4.87/5.03 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[206, 205])).
% 4.87/5.03 tff(208,plain,
% 4.87/5.03 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[207, 203])).
% 4.87/5.03 tff(209,plain,(
% 4.87/5.03 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))) | (k1_struct_0(A, B) = k1_tarski(B)))),
% 4.87/5.03 inference(skolemize,[status(sab)],[208])).
% 4.87/5.03 tff(210,plain,
% 4.87/5.03 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[209, 202])).
% 4.87/5.03 tff(211,plain,
% 4.87/5.03 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.87/5.03 inference(modus_ponens,[status(thm)],[210, 200])).
% 4.87/5.03 tff(212,plain,
% 4.87/5.03 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(213,plain,
% 4.87/5.04 ((v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1))) <=> (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(214,plain,
% 4.87/5.04 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[213])).
% 4.87/5.04 tff(215,plain,
% 4.87/5.04 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[214, 212])).
% 4.87/5.04 tff(216,plain,
% 4.87/5.04 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (~l1_struct_0(B!1)))),
% 4.87/5.04 inference(quant_inst,[status(thm)],[])).
% 4.87/5.04 tff(217,plain,
% 4.87/5.04 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[216, 215])).
% 4.87/5.04 tff(218,plain,
% 4.87/5.04 ((~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[217, 88, 211, 198])).
% 4.87/5.04 tff(219,plain,
% 4.87/5.04 (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[218, 173])).
% 4.87/5.04 tff(220,plain,
% 4.87/5.04 (k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.04 inference(symmetry,[status(thm)],[219])).
% 4.87/5.04 tff(221,plain,
% 4.87/5.04 (^[A: $i, B: $i, C: $i, D: $i] : refl((v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(222,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[221])).
% 4.87/5.04 tff(223,plain,
% 4.87/5.04 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(224,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[223])).
% 4.87/5.04 tff(225,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(226,plain,
% 4.87/5.04 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(227,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[226])).
% 4.87/5.04 tff(228,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 4.87/5.04 tff(229,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[228, 227])).
% 4.87/5.04 tff(230,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[229, 225])).
% 4.87/5.04 tff(231,plain,(
% 4.87/5.04 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 4.87/5.04 inference(skolemize,[status(sab)],[230])).
% 4.87/5.04 tff(232,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[231, 224])).
% 4.87/5.04 tff(233,plain,
% 4.87/5.04 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[232, 222])).
% 4.87/5.04 tff(234,plain,
% 4.87/5.04 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(235,plain,
% 4.87/5.04 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(236,plain,
% 4.87/5.04 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[235])).
% 4.87/5.04 tff(237,plain,
% 4.87/5.04 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[236, 234])).
% 4.87/5.04 tff(238,plain,
% 4.87/5.04 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))))),
% 4.87/5.04 inference(quant_inst,[status(thm)],[])).
% 4.87/5.04 tff(239,plain,
% 4.87/5.04 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[238, 237])).
% 4.87/5.04 tff(240,plain,
% 4.87/5.04 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[239, 96, 95, 233, 153, 118, 106])).
% 4.87/5.04 tff(241,plain,
% 4.87/5.04 (k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))),
% 4.87/5.04 inference(symmetry,[status(thm)],[240])).
% 4.87/5.04 tff(242,plain,
% 4.87/5.04 (k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[241])).
% 4.87/5.04 tff(243,plain,
% 4.87/5.04 (m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) <=> m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[241])).
% 4.87/5.04 tff(244,plain,
% 4.87/5.04 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) <=> m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.04 inference(symmetry,[status(thm)],[243])).
% 4.87/5.04 tff(245,plain,
% 4.87/5.04 (m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[173, 244])).
% 4.87/5.04 tff(246,plain,
% 4.87/5.04 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(247,plain,
% 4.87/5.04 ((v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1))) <=> (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(248,plain,
% 4.87/5.04 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[247])).
% 4.87/5.04 tff(249,plain,
% 4.87/5.04 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[248, 246])).
% 4.87/5.04 tff(250,plain,
% 4.87/5.04 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(B!1) | (~v1_xboole_0(u1_struct_0(B!1))) | (~l1_struct_0(B!1)))),
% 4.87/5.04 inference(quant_inst,[status(thm)],[])).
% 4.87/5.04 tff(251,plain,
% 4.87/5.04 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[250, 249])).
% 4.87/5.04 tff(252,plain,
% 4.87/5.04 ((~l1_struct_0(B!1)) | (~v1_xboole_0(u1_struct_0(B!1)))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[251, 88, 145])).
% 4.87/5.04 tff(253,plain,
% 4.87/5.04 (~v1_xboole_0(u1_struct_0(B!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[252, 198])).
% 4.87/5.04 tff(254,plain,
% 4.87/5.04 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(255,plain,
% 4.87/5.04 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[254])).
% 4.87/5.04 tff(256,plain,
% 4.87/5.04 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(257,plain,
% 4.87/5.04 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(258,plain,
% 4.87/5.04 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[257])).
% 4.87/5.04 tff(259,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 4.87/5.04 tff(260,plain,
% 4.87/5.04 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[259, 258])).
% 4.87/5.04 tff(261,plain,
% 4.87/5.04 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[260, 256])).
% 4.87/5.04 tff(262,plain,(
% 4.87/5.04 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(skolemize,[status(sab)],[261])).
% 4.87/5.04 tff(263,plain,
% 4.87/5.04 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[262, 255])).
% 4.87/5.04 tff(264,plain,
% 4.87/5.04 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(265,plain,
% 4.87/5.04 ((r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))) <=> (v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 4.87/5.04 inference(rewrite,[status(thm)],[])).
% 4.87/5.04 tff(266,plain,
% 4.87/5.04 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))))),
% 4.87/5.04 inference(monotonicity,[status(thm)],[265])).
% 4.87/5.04 tff(267,plain,
% 4.87/5.04 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)))),
% 4.87/5.04 inference(transitivity,[status(thm)],[266, 264])).
% 4.87/5.04 tff(268,plain,
% 4.87/5.04 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))))),
% 4.87/5.04 inference(quant_inst,[status(thm)],[])).
% 4.87/5.04 tff(269,plain,
% 4.87/5.04 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(B!1)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.04 inference(modus_ponens,[status(thm)],[268, 267])).
% 4.87/5.04 tff(270,plain,
% 4.87/5.04 ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[269, 263, 253])).
% 4.87/5.04 tff(271,plain,
% 4.87/5.04 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))),
% 4.87/5.04 inference(unit_resolution,[status(thm)],[270, 245])).
% 4.87/5.04 tff(272,plain,
% 4.87/5.04 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(273,plain,
% 4.87/5.04 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[272])).
% 4.87/5.04 tff(274,plain,
% 4.87/5.04 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(275,plain,
% 4.87/5.04 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[274])).
% 4.87/5.04 tff(276,plain,
% 4.87/5.04 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 4.87/5.04 inference(transitivity,[status(thm)],[275, 273])).
% 4.87/5.04 tff(277,plain,
% 4.87/5.04 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))))),
% 4.87/5.04 inference(bind,[status(th)],[])).
% 4.87/5.04 tff(278,plain,
% 4.87/5.04 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 4.87/5.04 inference(quant_intro,[status(thm)],[277])).
% 4.87/5.05 tff(279,plain,
% 4.87/5.05 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(280,plain,
% 4.87/5.05 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(281,plain,
% 4.87/5.05 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[280])).
% 4.87/5.05 tff(282,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 4.87/5.05 tff(283,plain,
% 4.87/5.05 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[282, 281])).
% 4.87/5.05 tff(284,plain,
% 4.87/5.05 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[283, 279])).
% 4.87/5.05 tff(285,plain,(
% 4.87/5.05 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))),
% 4.87/5.05 inference(skolemize,[status(sab)],[284])).
% 4.87/5.05 tff(286,plain,
% 4.87/5.05 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[285, 278])).
% 4.87/5.05 tff(287,plain,
% 4.87/5.05 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[286, 276])).
% 4.87/5.05 tff(288,plain,
% 4.87/5.05 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_4(B, A), A)) | r2_hidden(tptp_fun_C_4(B, A), B)))))))) | (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~(r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)) | (~((~r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(B!1))) | r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(A!0))))))))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(289,plain,
% 4.87/5.05 (~((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~(r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)) | (~((~r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(B!1))) | r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(A!0)))))))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[288, 287])).
% 4.87/5.05 tff(290,plain,
% 4.87/5.05 (((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~(r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)) | (~((~r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(B!1))) | r2_hidden(tptp_fun_C_4(u1_struct_0(A!0), u1_struct_0(B!1)), u1_struct_0(A!0))))))) | ((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))),
% 4.87/5.05 inference(tautology,[status(thm)],[])).
% 4.87/5.05 tff(291,plain,
% 4.87/5.05 ((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[290, 289])).
% 4.87/5.05 tff(292,plain,
% 4.87/5.05 (^[A: $i, B: $i] : refl((m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(293,plain,
% 4.87/5.05 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[292])).
% 4.87/5.05 tff(294,plain,
% 4.87/5.05 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(295,axiom,(![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 4.87/5.05 tff(296,plain,
% 4.87/5.05 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[295, 294])).
% 4.87/5.05 tff(297,plain,(
% 4.87/5.05 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 4.87/5.05 inference(skolemize,[status(sab)],[296])).
% 4.87/5.05 tff(298,plain,
% 4.87/5.05 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[297, 293])).
% 4.87/5.05 tff(299,plain,
% 4.87/5.05 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(300,plain,
% 4.87/5.05 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[299, 298])).
% 4.87/5.05 tff(301,plain,
% 4.87/5.05 ((~(m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 4.87/5.05 inference(tautology,[status(thm)],[])).
% 4.87/5.05 tff(302,plain,
% 4.87/5.05 ((~(m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0)))) | r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[301, 61])).
% 4.87/5.05 tff(303,plain,
% 4.87/5.05 (r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[302, 300])).
% 4.87/5.05 tff(304,plain,
% 4.87/5.05 ((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | (~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 4.87/5.05 inference(tautology,[status(thm)],[])).
% 4.87/5.05 tff(305,plain,
% 4.87/5.05 ((~((~r1_tarski(u1_struct_0(B!1), u1_struct_0(A!0))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0))))) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[304, 303])).
% 4.87/5.05 tff(306,plain,
% 4.87/5.05 (![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[305, 291])).
% 4.87/5.05 tff(307,plain,
% 4.87/5.05 (((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(308,plain,
% 4.87/5.05 ((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(309,plain,
% 4.87/5.05 ((~![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | r2_hidden(C, u1_struct_0(A!0)))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[308, 307])).
% 4.87/5.05 tff(310,plain,
% 4.87/5.05 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[309, 306, 271])).
% 4.87/5.05 tff(311,plain,
% 4.87/5.05 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(312,plain,
% 4.87/5.05 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[311])).
% 4.87/5.05 tff(313,plain,
% 4.87/5.05 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(314,plain,
% 4.87/5.05 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(315,plain,
% 4.87/5.05 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[314])).
% 4.87/5.05 tff(316,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 4.87/5.05 tff(317,plain,
% 4.87/5.05 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[316, 315])).
% 4.87/5.05 tff(318,plain,
% 4.87/5.05 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[317, 313])).
% 4.87/5.05 tff(319,plain,(
% 4.87/5.05 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(skolemize,[status(sab)],[318])).
% 4.87/5.05 tff(320,plain,
% 4.87/5.05 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[319, 312])).
% 4.87/5.05 tff(321,plain,
% 4.87/5.05 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(322,plain,
% 4.87/5.05 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0)))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(323,plain,
% 4.87/5.05 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[322, 321])).
% 4.87/5.05 tff(324,plain,
% 4.87/5.05 (m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[323, 320, 310])).
% 4.87/5.05 tff(325,plain,
% 4.87/5.05 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(326,plain,
% 4.87/5.05 ((v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(327,plain,
% 4.87/5.05 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[326])).
% 4.87/5.05 tff(328,plain,
% 4.87/5.05 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[327, 325])).
% 4.87/5.05 tff(329,plain,
% 4.87/5.05 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 4.87/5.05 inference(quant_inst,[status(thm)],[])).
% 4.87/5.05 tff(330,plain,
% 4.87/5.05 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[329, 328])).
% 4.87/5.05 tff(331,plain,
% 4.87/5.05 (k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k1_tarski(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.05 inference(unit_resolution,[status(thm)],[330, 79, 211, 132, 324])).
% 4.87/5.05 tff(332,plain,
% 4.87/5.05 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(333,plain,
% 4.87/5.05 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[332])).
% 4.87/5.05 tff(334,plain,
% 4.87/5.05 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(335,plain,
% 4.87/5.05 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[334])).
% 4.87/5.05 tff(336,plain,
% 4.87/5.05 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[335, 333])).
% 4.87/5.05 tff(337,plain,
% 4.87/5.05 (^[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] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(338,plain,
% 4.87/5.05 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[337])).
% 4.87/5.05 tff(339,plain,
% 4.87/5.05 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(340,plain,
% 4.87/5.05 (^[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((v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))) <=> (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))))),
% 4.87/5.05 inference(bind,[status(th)],[])).
% 4.87/5.05 tff(341,plain,
% 4.87/5.05 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 4.87/5.05 inference(quant_intro,[status(thm)],[340])).
% 4.87/5.05 tff(342,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_1(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) => (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tsp_2')).
% 4.87/5.05 tff(343,plain,
% 4.87/5.05 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[342, 341])).
% 4.87/5.05 tff(344,plain,
% 4.87/5.05 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_1(B, A) <=> ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[343, 339])).
% 4.87/5.05 tff(345,plain,(
% 4.87/5.05 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A))))) & (v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))),
% 4.87/5.05 inference(skolemize,[status(sab)],[344])).
% 4.87/5.05 tff(346,plain,
% 4.87/5.05 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[345, 338])).
% 4.87/5.05 tff(347,plain,
% 4.87/5.05 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))),
% 4.87/5.05 inference(modus_ponens,[status(thm)],[346, 336])).
% 4.87/5.05 tff(348,plain,
% 4.87/5.05 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(349,plain,
% 4.87/5.05 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))))))))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))),
% 4.87/5.05 inference(rewrite,[status(thm)],[])).
% 4.87/5.05 tff(350,plain,
% 4.87/5.05 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))))),
% 4.87/5.05 inference(monotonicity,[status(thm)],[349])).
% 4.87/5.05 tff(351,plain,
% 4.87/5.05 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B))))))))))),
% 4.87/5.05 inference(transitivity,[status(thm)],[350, 348])).
% 4.87/5.05 tff(352,plain,
% 4.87/5.05 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)) | (~m1_subset_1(C, u1_struct_0(A!0)))))) | (~(v1_tsp_1(B, A!0) | (~((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0)))))))))))),
% 4.87/5.06 inference(quant_inst,[status(thm)],[])).
% 4.87/5.06 tff(353,plain,
% 4.87/5.06 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_1(B, A)) | ![C: $i] : ((~r2_hidden(C, B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, C)) = k1_struct_0(A, C)) | (~m1_subset_1(C, u1_struct_0(A)))))) | (~(v1_tsp_1(B, A) | (~((~r2_hidden(tptp_fun_C_3(B, A), B)) | (k5_subset_1(u1_struct_0(A), B, k4_tex_4(A, tptp_fun_C_3(B, A))) = k1_struct_0(A, tptp_fun_C_3(B, A))) | (~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[352, 351])).
% 4.87/5.06 tff(354,plain,
% 4.87/5.06 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[353, 79, 78, 29, 347])).
% 4.87/5.06 tff(355,plain,
% 4.87/5.06 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(356,plain,
% 4.87/5.06 (((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1)))))))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(357,plain,
% 4.87/5.06 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))))))),
% 4.87/5.06 inference(monotonicity,[status(thm)],[356])).
% 4.87/5.06 tff(358,plain,
% 4.87/5.06 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))))),
% 4.87/5.06 inference(transitivity,[status(thm)],[357, 355])).
% 4.87/5.06 tff(359,plain,
% 4.87/5.06 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~r2_hidden(C, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))))))))))),
% 4.87/5.06 inference(quant_inst,[status(thm)],[])).
% 4.87/5.06 tff(360,plain,
% 4.87/5.06 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | ![C: $i] : ((~r2_hidden(C, B)) | (~m1_subset_1(C, u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), B, k4_tex_4(A!0, tptp_fun_C_3(B, A!0))) = k1_struct_0(A!0, tptp_fun_C_3(B, A!0))) | (~r2_hidden(tptp_fun_C_3(B, A!0), B)))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[359, 358])).
% 4.87/5.06 tff(361,plain,
% 4.87/5.06 (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0))))))))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[360, 354, 61])).
% 4.87/5.06 tff(362,plain,
% 4.87/5.06 (((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~(v1_tsp_1(u1_struct_0(B!1), A!0) | (~((~r2_hidden(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) = k1_struct_0(A!0, tptp_fun_C_3(u1_struct_0(B!1), A!0))) | (~m1_subset_1(tptp_fun_C_3(u1_struct_0(B!1), A!0), u1_struct_0(A!0)))))))) | ((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))),
% 4.87/5.06 inference(tautology,[status(thm)],[])).
% 4.87/5.06 tff(363,plain,
% 4.87/5.06 ((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))),
% 4.87/5.06 inference(unit_resolution,[status(thm)],[362, 361])).
% 4.87/5.06 tff(364,plain,
% 4.87/5.06 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))))))))),
% 4.87/5.06 inference(bind,[status(th)],[])).
% 4.87/5.06 tff(365,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))),
% 4.87/5.06 inference(quant_intro,[status(thm)],[364])).
% 4.87/5.06 tff(366,plain,
% 4.87/5.06 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))))),
% 4.87/5.06 inference(bind,[status(th)],[])).
% 4.87/5.06 tff(367,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 4.87/5.06 inference(quant_intro,[status(thm)],[366])).
% 4.87/5.06 tff(368,plain,
% 4.87/5.06 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))))),
% 4.87/5.06 inference(bind,[status(th)],[])).
% 4.87/5.06 tff(369,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 4.87/5.06 inference(quant_intro,[status(thm)],[368])).
% 4.87/5.06 tff(370,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 4.87/5.06 inference(transitivity,[status(thm)],[369, 367])).
% 4.87/5.06 tff(371,plain,
% 4.87/5.06 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))))))))),
% 4.87/5.06 inference(bind,[status(th)],[])).
% 4.87/5.06 tff(372,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 4.87/5.06 inference(quant_intro,[status(thm)],[371])).
% 4.87/5.06 tff(373,plain,
% 4.87/5.06 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 4.87/5.06 inference(bind,[status(th)],[])).
% 4.87/5.06 tff(374,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))),
% 4.87/5.06 inference(quant_intro,[status(thm)],[373])).
% 4.87/5.06 tff(375,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(376,plain,
% 4.87/5.06 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))) <=> (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), ((l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), ((l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 4.87/5.06 inference(bind,[status(th)],[])).
% 4.87/5.06 tff(377,plain,
% 4.87/5.06 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C))))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 4.87/5.06 inference(quant_intro,[status(thm)],[376])).
% 4.87/5.06 tff(378,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((v1_tsp_1(C, A) & r1_tarski(B, C)) => (B = C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tsp_2')).
% 4.87/5.06 tff(379,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[378, 377])).
% 4.87/5.06 tff(380,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[379, 375])).
% 4.87/5.06 tff(381,plain,(
% 4.87/5.06 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | ((~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))),
% 4.87/5.06 inference(skolemize,[status(sab)],[380])).
% 4.87/5.06 tff(382,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~v1_tsp_2(B, A)) | (v1_tsp_1(B, A) & ![C: $i] : ((B = C) | (~(v1_tsp_1(C, A) & r1_tarski(B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) & (v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~(v1_tsp_1(tptp_fun_C_5(B, A), A) & r1_tarski(B, tptp_fun_C_5(B, A)))) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A))))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[381, 374])).
% 4.87/5.06 tff(383,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[382, 372])).
% 4.87/5.06 tff(384,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A)))))))) | (~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A)))))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[383, 370])).
% 4.87/5.06 tff(385,plain,
% 4.87/5.06 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))),
% 4.87/5.06 inference(modus_ponens,[status(thm)],[384, 365])).
% 4.87/5.06 tff(386,plain,
% 4.87/5.06 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0))))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0))))))))))))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(387,plain,
% 4.87/5.06 (((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)))))))))))) <=> ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0))))))))))))))),
% 4.87/5.06 inference(rewrite,[status(thm)],[])).
% 4.87/5.06 tff(388,plain,
% 4.87/5.06 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[387])).
% 4.87/5.07 tff(389,plain,
% 4.87/5.07 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0))))))))))))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[388, 386])).
% 4.87/5.07 tff(390,plain,
% 4.87/5.07 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(B, A!0) | (~v1_tsp_1(B, A!0)) | (~((B = tptp_fun_C_5(B, A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~r1_tarski(B, tptp_fun_C_5(B, A!0))))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0))))))))))))),
% 4.87/5.07 inference(quant_inst,[status(thm)],[])).
% 4.87/5.07 tff(391,plain,
% 4.87/5.07 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(v1_tsp_2(B, A) | (~v1_tsp_1(B, A)) | (~((B = tptp_fun_C_5(B, A)) | (~m1_subset_1(tptp_fun_C_5(B, A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_tsp_1(tptp_fun_C_5(B, A), A)) | (~r1_tarski(B, tptp_fun_C_5(B, A))))))) | (~((~v1_tsp_2(B, A)) | (~((~v1_tsp_1(B, A)) | (~![C: $i] : ((B = C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A))))))))))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[390, 389])).
% 4.87/5.07 tff(392,plain,
% 4.87/5.07 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[391, 29, 385])).
% 4.87/5.07 tff(393,plain,
% 4.87/5.07 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(394,plain,
% 4.87/5.07 (((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | v1_tsp_2(u1_struct_0(B!1), A!0) | (~((~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0))))))))))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(395,plain,
% 4.87/5.07 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | v1_tsp_2(u1_struct_0(B!1), A!0) | (~((~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))))))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[394])).
% 4.87/5.07 tff(396,plain,
% 4.87/5.07 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | v1_tsp_2(u1_struct_0(B!1), A!0) | (~((~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[395, 393])).
% 4.87/5.07 tff(397,plain,
% 4.87/5.07 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | v1_tsp_2(u1_struct_0(B!1), A!0) | (~((~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))),
% 4.87/5.07 inference(quant_inst,[status(thm)],[])).
% 4.87/5.07 tff(398,plain,
% 4.87/5.07 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~v1_tsp_1(B, A!0)) | v1_tsp_2(B, A!0) | (~((~r1_tarski(B, tptp_fun_C_5(B, A!0))) | (~v1_tsp_1(tptp_fun_C_5(B, A!0), A!0)) | (~m1_subset_1(tptp_fun_C_5(B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (B = tptp_fun_C_5(B, A!0)))))) | (~((~v1_tsp_2(B, A!0)) | (~((~v1_tsp_1(B, A!0)) | (~![C: $i] : ((B = C) | (~r1_tarski(B, C)) | (~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[397, 396])).
% 4.87/5.07 tff(399,plain,
% 4.87/5.07 (~((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[398, 392, 61])).
% 4.87/5.07 tff(400,plain,
% 4.87/5.07 (((~(v1_tsp_2(u1_struct_0(B!1), A!0) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~((u1_struct_0(B!1) = tptp_fun_C_5(u1_struct_0(B!1), A!0)) | (~m1_subset_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_tsp_1(tptp_fun_C_5(u1_struct_0(B!1), A!0), A!0)) | (~r1_tarski(u1_struct_0(B!1), tptp_fun_C_5(u1_struct_0(B!1), A!0))))))) | (~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))))) | ((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))),
% 4.87/5.07 inference(tautology,[status(thm)],[])).
% 4.87/5.07 tff(401,plain,
% 4.87/5.07 ((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[400, 399])).
% 4.87/5.07 tff(402,plain,
% 4.87/5.07 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 4.87/5.07 inference(bind,[status(th)],[])).
% 4.87/5.07 tff(403,plain,
% 4.87/5.07 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(quant_intro,[status(thm)],[402])).
% 4.87/5.07 tff(404,plain,
% 4.87/5.07 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 4.87/5.07 inference(bind,[status(th)],[])).
% 4.87/5.07 tff(405,plain,
% 4.87/5.07 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(quant_intro,[status(thm)],[404])).
% 4.87/5.07 tff(406,plain,
% 4.87/5.07 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(transitivity,[status(thm)],[405, 403])).
% 4.87/5.07 tff(407,plain,
% 4.87/5.07 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))),
% 4.87/5.07 inference(bind,[status(th)],[])).
% 4.87/5.07 tff(408,plain,
% 4.87/5.07 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(quant_intro,[status(thm)],[407])).
% 4.87/5.07 tff(409,plain,
% 4.87/5.07 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(410,plain,
% 4.87/5.07 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))) <=> ((~(C = u1_struct_0(B))) | (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~(C = u1_struct_0(B))) | (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~(C = u1_struct_0(B))) | (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))))), trans(der(![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))) <=> ![C: $i] : ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), elim_unused(![C: $i] : ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), (![C: $i] : ((v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~(C = u1_struct_0(B)))) <=> ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))) <=> ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), ((m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))) <=> (m2_tsp_1(B, A) => ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((m2_tsp_1(B, A) => ((v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))) <=> ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))), (![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))) <=> ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))))),
% 4.87/5.07 inference(bind,[status(th)],[])).
% 4.87/5.07 tff(411,plain,
% 4.87/5.07 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(quant_intro,[status(thm)],[410])).
% 4.87/5.07 tff(412,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m2_tsp_1(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((C = u1_struct_0(B)) => (v1_tsp_2(C, A) <=> v2_tsp_2(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t11_tsp_2')).
% 4.87/5.07 tff(413,plain,
% 4.87/5.07 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[412, 411])).
% 4.87/5.07 tff(414,plain,
% 4.87/5.07 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[413, 409])).
% 4.87/5.07 tff(415,plain,(
% 4.87/5.07 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(skolemize,[status(sab)],[414])).
% 4.87/5.07 tff(416,plain,
% 4.87/5.07 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[415, 408])).
% 4.87/5.07 tff(417,plain,
% 4.87/5.07 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[416, 406])).
% 4.87/5.07 tff(418,plain,
% 4.87/5.07 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(419,plain,
% 4.87/5.07 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 4.87/5.07 inference(quant_inst,[status(thm)],[])).
% 4.87/5.07 tff(420,plain,
% 4.87/5.07 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m2_tsp_1(B, A)) | (v1_tsp_2(u1_struct_0(B), A) <=> v2_tsp_2(B, A)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[419, 418])).
% 4.87/5.07 tff(421,plain,
% 4.87/5.07 (![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[420, 79, 29, 417])).
% 4.87/5.07 tff(422,plain,
% 4.87/5.07 (((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))) <=> ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(423,plain,
% 4.87/5.07 (((~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 4.87/5.07 inference(rewrite,[status(thm)],[])).
% 4.87/5.07 tff(424,plain,
% 4.87/5.07 (((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | ((~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))))),
% 4.87/5.07 inference(monotonicity,[status(thm)],[423])).
% 4.87/5.07 tff(425,plain,
% 4.87/5.07 (((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | ((~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)))),
% 4.87/5.07 inference(transitivity,[status(thm)],[424, 422])).
% 4.87/5.07 tff(426,plain,
% 4.87/5.07 ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | ((~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.87/5.07 inference(quant_inst,[status(thm)],[])).
% 4.87/5.07 tff(427,plain,
% 4.87/5.07 ((~![B: $i] : ((~m2_tsp_1(B, A!0)) | (v1_tsp_2(u1_struct_0(B), A!0) <=> v2_tsp_2(B, A!0)) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_tsp_1(B!1, A!0)) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))),
% 4.87/5.07 inference(modus_ponens,[status(thm)],[426, 425])).
% 4.87/5.07 tff(428,plain,
% 4.87/5.07 ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[427, 36, 421])).
% 4.87/5.07 tff(429,plain,
% 4.87/5.07 (v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[428, 61])).
% 4.87/5.07 tff(430,plain,
% 4.87/5.07 ((~(v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) | v1_tsp_2(u1_struct_0(B!1), A!0) | (~v2_tsp_2(B!1, A!0))),
% 4.87/5.07 inference(tautology,[status(thm)],[])).
% 4.87/5.07 tff(431,plain,
% 4.87/5.07 ((~(v1_tsp_2(u1_struct_0(B!1), A!0) <=> v2_tsp_2(B!1, A!0))) | v1_tsp_2(u1_struct_0(B!1), A!0)),
% 4.87/5.07 inference(unit_resolution,[status(thm)],[430, 87])).
% 4.87/5.08 tff(432,plain,
% 4.87/5.08 (v1_tsp_2(u1_struct_0(B!1), A!0)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[431, 429])).
% 4.87/5.08 tff(433,plain,
% 4.87/5.08 ((~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))) | (~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))),
% 4.87/5.08 inference(tautology,[status(thm)],[])).
% 4.87/5.08 tff(434,plain,
% 4.87/5.08 ((~((~v1_tsp_2(u1_struct_0(B!1), A!0)) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))))) | (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[433, 432])).
% 4.87/5.08 tff(435,plain,
% 4.87/5.08 (~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C)))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[434, 401])).
% 4.87/5.08 tff(436,plain,
% 4.87/5.08 (((~v1_tsp_1(u1_struct_0(B!1), A!0)) | (~![C: $i] : ((~v1_tsp_1(C, A!0)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (u1_struct_0(B!1) = C) | (~r1_tarski(u1_struct_0(B!1), C))))) | v1_tsp_1(u1_struct_0(B!1), A!0)),
% 4.87/5.08 inference(tautology,[status(thm)],[])).
% 4.87/5.08 tff(437,plain,
% 4.87/5.08 (v1_tsp_1(u1_struct_0(B!1), A!0)),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[436, 435])).
% 4.87/5.08 tff(438,plain,
% 4.87/5.08 ((~((~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C))))) | (~v1_tsp_1(u1_struct_0(B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))),
% 4.87/5.08 inference(tautology,[status(thm)],[])).
% 4.87/5.08 tff(439,plain,
% 4.87/5.08 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[438, 437, 363])).
% 4.87/5.08 tff(440,plain,
% 4.87/5.08 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(441,plain,
% 4.87/5.08 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.08 inference(quant_inst,[status(thm)],[])).
% 4.87/5.08 tff(442,plain,
% 4.87/5.08 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, C)) = k1_struct_0(A!0, C)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(B!1))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[441, 440])).
% 4.87/5.08 tff(443,plain,
% 4.87/5.08 ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[442, 439, 271])).
% 4.87/5.08 tff(444,plain,
% 4.87/5.08 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) = k1_struct_0(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[443, 324])).
% 4.87/5.08 tff(445,plain,
% 4.87/5.08 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(446,plain,
% 4.87/5.08 (![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[445])).
% 4.87/5.08 tff(447,plain,
% 4.87/5.08 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k4_tex_4(A, B) = k2_tex_4(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(448,plain,
% 4.87/5.08 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[447])).
% 4.87/5.08 tff(449,plain,
% 4.87/5.08 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(450,plain,
% 4.87/5.08 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(451,plain,
% 4.87/5.08 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[450])).
% 4.87/5.08 tff(452,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => (k4_tex_4(A, B) = k2_tex_4(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_tex_4')).
% 4.87/5.08 tff(453,plain,
% 4.87/5.08 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[452, 451])).
% 4.87/5.08 tff(454,plain,
% 4.87/5.08 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[453, 449])).
% 4.87/5.08 tff(455,plain,(
% 4.87/5.08 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | (k4_tex_4(A, B) = k2_tex_4(A, B)))),
% 4.87/5.08 inference(skolemize,[status(sab)],[454])).
% 4.87/5.08 tff(456,plain,
% 4.87/5.08 (![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[455, 448])).
% 4.87/5.08 tff(457,plain,
% 4.87/5.08 (![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[456, 446])).
% 4.87/5.08 tff(458,plain,
% 4.87/5.08 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(459,plain,
% 4.87/5.08 ((v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(460,plain,
% 4.87/5.08 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[459])).
% 4.87/5.08 tff(461,plain,
% 4.87/5.08 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.08 inference(transitivity,[status(thm)],[460, 458])).
% 4.87/5.08 tff(462,plain,
% 4.87/5.08 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 4.87/5.08 inference(quant_inst,[status(thm)],[])).
% 4.87/5.08 tff(463,plain,
% 4.87/5.08 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[462, 461])).
% 4.87/5.08 tff(464,plain,
% 4.87/5.08 (k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[463, 79, 78, 29, 457, 324])).
% 4.87/5.08 tff(465,plain,
% 4.87/5.08 (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(symmetry,[status(thm)],[464])).
% 4.87/5.08 tff(466,plain,
% 4.87/5.08 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(467,plain,
% 4.87/5.08 ((v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(468,plain,
% 4.87/5.08 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[467])).
% 4.87/5.08 tff(469,plain,
% 4.87/5.08 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(transitivity,[status(thm)],[468, 466])).
% 4.87/5.08 tff(470,plain,
% 4.87/5.08 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 4.87/5.08 inference(quant_inst,[status(thm)],[])).
% 4.87/5.08 tff(471,plain,
% 4.87/5.08 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k4_tex_4(A, B) = k2_tex_4(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[470, 469])).
% 4.87/5.08 tff(472,plain,
% 4.87/5.08 (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[471, 79, 78, 29, 457, 106])).
% 4.87/5.08 tff(473,plain,
% 4.87/5.08 (k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))),
% 4.87/5.08 inference(symmetry,[status(thm)],[472])).
% 4.87/5.08 tff(474,plain,
% 4.87/5.08 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(monotonicity,[status(thm)],[241, 473])).
% 4.87/5.08 tff(475,plain,
% 4.87/5.08 (r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(symmetry,[status(thm)],[474])).
% 4.87/5.08 tff(476,plain,
% 4.87/5.08 (^[D: $i] : refl(((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) <=> ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(477,plain,
% 4.87/5.08 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D))) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[476])).
% 4.87/5.08 tff(478,plain,
% 4.87/5.08 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))),
% 4.87/5.08 inference(and_elim,[status(thm)],[28])).
% 4.87/5.08 tff(479,plain,
% 4.87/5.08 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[478, 477])).
% 4.87/5.08 tff(480,plain,
% 4.87/5.08 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | ((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(481,plain,
% 4.87/5.08 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | ((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.87/5.08 inference(quant_inst,[status(thm)],[])).
% 4.87/5.08 tff(482,plain,
% 4.87/5.08 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, D), k4_tex_4(A!0, D)))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[481, 480])).
% 4.87/5.08 tff(483,plain,
% 4.87/5.08 (r2_hidden(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(unit_resolution,[status(thm)],[482, 479, 106])).
% 4.87/5.08 tff(484,plain,
% 4.87/5.08 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[483, 475])).
% 4.87/5.08 tff(485,plain,
% 4.87/5.08 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(486,plain,
% 4.87/5.08 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[485])).
% 4.87/5.08 tff(487,plain,
% 4.87/5.08 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(488,plain,
% 4.87/5.08 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[487])).
% 4.87/5.08 tff(489,plain,
% 4.87/5.08 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(transitivity,[status(thm)],[488, 486])).
% 4.87/5.08 tff(490,plain,
% 4.87/5.08 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(491,plain,
% 4.87/5.08 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[490])).
% 4.87/5.08 tff(492,plain,
% 4.87/5.08 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(493,plain,
% 4.87/5.08 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))))),
% 4.87/5.08 inference(bind,[status(th)],[])).
% 4.87/5.08 tff(494,plain,
% 4.87/5.08 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(quant_intro,[status(thm)],[493])).
% 4.87/5.08 tff(495,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_tex_4')).
% 4.87/5.08 tff(496,plain,
% 4.87/5.08 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[495, 494])).
% 4.87/5.08 tff(497,plain,
% 4.87/5.08 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[496, 492])).
% 4.87/5.08 tff(498,plain,(
% 4.87/5.08 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(skolemize,[status(sab)],[497])).
% 4.87/5.08 tff(499,plain,
% 4.87/5.08 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[498, 491])).
% 4.87/5.08 tff(500,plain,
% 4.87/5.08 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))),
% 4.87/5.08 inference(modus_ponens,[status(thm)],[499, 489])).
% 4.87/5.08 tff(501,plain,
% 4.87/5.08 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B))))))),
% 4.87/5.08 inference(rewrite,[status(thm)],[])).
% 4.87/5.08 tff(502,plain,
% 4.87/5.08 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B))))))),
% 4.94/5.09 inference(quant_inst,[status(thm)],[])).
% 4.94/5.09 tff(503,plain,
% 4.94/5.09 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k2_tex_4(A, B)) <=> (k2_tex_4(A, C) = k2_tex_4(A, B))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))),
% 4.94/5.09 inference(modus_ponens,[status(thm)],[502, 501])).
% 4.94/5.09 tff(504,plain,
% 4.94/5.09 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))),
% 4.94/5.09 inference(unit_resolution,[status(thm)],[503, 79, 29, 500])).
% 4.94/5.09 tff(505,plain,
% 4.94/5.09 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | ((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))))),
% 4.94/5.09 inference(rewrite,[status(thm)],[])).
% 4.94/5.09 tff(506,plain,
% 4.94/5.09 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | ((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))))),
% 4.94/5.09 inference(quant_inst,[status(thm)],[])).
% 4.94/5.09 tff(507,plain,
% 4.94/5.09 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, B)) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, B)))))) | (~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.94/5.09 inference(modus_ponens,[status(thm)],[506, 505])).
% 4.94/5.09 tff(508,plain,
% 4.94/5.09 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.94/5.09 inference(unit_resolution,[status(thm)],[507, 504, 106])).
% 4.94/5.09 tff(509,plain,
% 4.94/5.09 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.94/5.09 inference(rewrite,[status(thm)],[])).
% 4.94/5.09 tff(510,plain,
% 4.94/5.09 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))) | ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.94/5.09 inference(quant_inst,[status(thm)],[])).
% 4.94/5.09 tff(511,plain,
% 4.94/5.09 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, C) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))))) | (~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.94/5.09 inference(modus_ponens,[status(thm)],[510, 509])).
% 4.94/5.09 tff(512,plain,
% 4.94/5.09 ((~m1_subset_1(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), u1_struct_0(A!0))) | (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.94/5.09 inference(unit_resolution,[status(thm)],[511, 508])).
% 4.94/5.09 tff(513,plain,
% 4.94/5.09 (r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.94/5.09 inference(unit_resolution,[status(thm)],[512, 324])).
% 4.94/5.09 tff(514,plain,
% 4.94/5.09 ((~(r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) <=> (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))))) | (~r2_hidden(k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)), k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))) | (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.94/5.09 inference(tautology,[status(thm)],[])).
% 4.94/5.09 tff(515,plain,
% 4.94/5.09 (k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))) = k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))),
% 4.94/5.09 inference(unit_resolution,[status(thm)],[514, 513, 484])).
% 4.94/5.09 tff(516,plain,
% 4.94/5.09 (k2_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k2_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.94/5.09 inference(symmetry,[status(thm)],[515])).
% 4.94/5.09 tff(517,plain,
% 4.94/5.09 (k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0)) = k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.94/5.09 inference(transitivity,[status(thm)],[472, 516, 465])).
% 4.94/5.09 tff(518,plain,
% 4.94/5.09 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, k1_funct_1(C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.94/5.09 inference(monotonicity,[status(thm)],[517])).
% 4.94/5.09 tff(519,plain,
% 4.94/5.09 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))),
% 4.94/5.09 inference(transitivity,[status(thm)],[518, 444, 331, 242, 220])).
% 4.94/5.09 tff(520,plain,
% 4.94/5.09 (((~m1_subset_1(tptp_fun_E_25(C!2, B!1, A!0), u1_struct_0(A!0))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))))) | (~(k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0)))))),
% 4.94/5.09 inference(tautology,[status(thm)],[])).
% 4.94/5.09 tff(521,plain,
% 4.94/5.09 (~(k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_tex_4(A!0, tptp_fun_E_25(C!2, B!1, A!0))) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, tptp_fun_E_25(C!2, B!1, A!0))))),
% 4.94/5.10 inference(unit_resolution,[status(thm)],[520, 104])).
% 4.94/5.10 tff(522,plain,
% 4.94/5.10 ($false),
% 4.94/5.10 inference(unit_resolution,[status(thm)],[521, 519])).
% 4.94/5.10 % SZS output end Proof
% 4.94/5.12 % E exiting
%------------------------------------------------------------------------------