%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP036+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 05:42:41 AM UTC 2025
% Result : Theorem 2.44s 2.60s
% Output : Proof 2.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP036+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:58:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.44/2.60 % SZS status Theorem
% 2.44/2.60 % SZS output start Proof
% 2.44/2.60 tff(v1_xboole_0_type, type, (
% 2.44/2.60 v1_xboole_0: $i > $o)).
% 2.44/2.60 tff(k4_tex_4_type, type, (
% 2.44/2.60 k4_tex_4: ( $i * $i ) > $i)).
% 2.44/2.60 tff(tptp_fun_C_2_type, type, (
% 2.44/2.60 tptp_fun_C_2: $i)).
% 2.44/2.60 tff(tptp_fun_A_0_type, type, (
% 2.44/2.60 tptp_fun_A_0: $i)).
% 2.44/2.60 tff(k1_xboole_0_type, type, (
% 2.44/2.60 k1_xboole_0: $i)).
% 2.44/2.60 tff(k2_tex_4_type, type, (
% 2.44/2.60 k2_tex_4: ( $i * $i ) > $i)).
% 2.44/2.60 tff(r1_tarski_type, type, (
% 2.44/2.60 r1_tarski: ( $i * $i ) > $o)).
% 2.44/2.60 tff(k1_relat_1_type, type, (
% 2.44/2.60 k1_relat_1: $i > $i)).
% 2.44/2.60 tff(k1_tsp_2_type, type, (
% 2.44/2.60 k1_tsp_2: ( $i * $i ) > $i)).
% 2.44/2.60 tff(tptp_fun_B_1_type, type, (
% 2.44/2.60 tptp_fun_B_1: $i)).
% 2.44/2.60 tff(u1_struct_0_type, type, (
% 2.44/2.60 u1_struct_0: $i > $i)).
% 2.44/2.60 tff(k2_pre_topc_type, type, (
% 2.44/2.60 k2_pre_topc: $i > $i)).
% 2.44/2.60 tff(l1_struct_0_type, type, (
% 2.44/2.60 l1_struct_0: $i > $o)).
% 2.44/2.60 tff(l1_pre_topc_type, type, (
% 2.44/2.60 l1_pre_topc: $i > $o)).
% 2.44/2.60 tff(k4_pre_topc_type, type, (
% 2.44/2.60 k4_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 2.44/2.60 tff(k3_tsp_2_type, type, (
% 2.44/2.60 k3_tsp_2: ( $i * $i ) > $i)).
% 2.44/2.60 tff(k1_struct_0_type, type, (
% 2.44/2.60 k1_struct_0: ( $i * $i ) > $i)).
% 2.44/2.60 tff(m1_subset_1_type, type, (
% 2.44/2.60 m1_subset_1: ( $i * $i ) > $o)).
% 2.44/2.60 tff(m2_tsp_1_type, type, (
% 2.44/2.60 m2_tsp_1: ( $i * $i ) > $o)).
% 2.44/2.60 tff(v2_tsp_2_type, type, (
% 2.44/2.60 v2_tsp_2: ( $i * $i ) > $o)).
% 2.44/2.60 tff(v3_struct_0_type, type, (
% 2.44/2.60 v3_struct_0: $i > $o)).
% 2.44/2.60 tff(v2_pre_topc_type, type, (
% 2.44/2.60 v2_pre_topc: $i > $o)).
% 2.44/2.60 tff(k2_relat_1_type, type, (
% 2.44/2.60 k2_relat_1: $i > $i)).
% 2.44/2.60 tff(m2_relset_1_type, type, (
% 2.44/2.60 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.44/2.60 tff(v1_funct_2_type, type, (
% 2.44/2.60 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.44/2.60 tff(v1_funct_1_type, type, (
% 2.44/2.60 v1_funct_1: $i > $o)).
% 2.44/2.60 tff(v5_pre_topc_type, type, (
% 2.44/2.60 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 2.44/2.60 tff(m1_pre_topc_type, type, (
% 2.44/2.60 m1_pre_topc: ( $i * $i ) > $o)).
% 2.44/2.60 tff(k1_zfmisc_1_type, type, (
% 2.44/2.60 k1_zfmisc_1: $i > $i)).
% 2.44/2.60 tff(k9_relat_1_type, type, (
% 2.44/2.60 k9_relat_1: ( $i * $i ) > $i)).
% 2.44/2.60 tff(k1_tarski_type, type, (
% 2.44/2.60 k1_tarski: $i > $i)).
% 2.44/2.60 tff(k1_funct_1_type, type, (
% 2.44/2.60 k1_funct_1: ( $i * $i ) > $i)).
% 2.44/2.60 tff(k8_funct_2_type, type, (
% 2.44/2.60 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 2.44/2.60 tff(k10_relat_1_type, type, (
% 2.44/2.60 k10_relat_1: ( $i * $i ) > $i)).
% 2.44/2.60 tff(m1_relset_1_type, type, (
% 2.44/2.60 m1_relset_1: ( $i * $i * $i ) > $o)).
% 2.44/2.60 tff(k5_pre_topc_type, type, (
% 2.44/2.60 k5_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 2.44/2.60 tff(v1_relat_1_type, type, (
% 2.44/2.60 v1_relat_1: $i > $o)).
% 2.44/2.60 tff(k2_zfmisc_1_type, type, (
% 2.44/2.60 k2_zfmisc_1: ( $i * $i ) > $i)).
% 2.44/2.60 tff(r2_hidden_type, type, (
% 2.44/2.60 r2_hidden: ( $i * $i ) > $o)).
% 2.44/2.60 tff(v1_membered_type, type, (
% 2.44/2.60 v1_membered: $i > $o)).
% 2.44/2.60 tff(v2_membered_type, type, (
% 2.44/2.60 v2_membered: $i > $o)).
% 2.44/2.60 tff(v3_membered_type, type, (
% 2.44/2.60 v3_membered: $i > $o)).
% 2.44/2.60 tff(v4_membered_type, type, (
% 2.44/2.60 v4_membered: $i > $o)).
% 2.44/2.60 tff(v5_membered_type, type, (
% 2.44/2.60 v5_membered: $i > $o)).
% 2.44/2.60 tff(1,plain,
% 2.44/2.60 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(2,plain,
% 2.44/2.60 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[1])).
% 2.44/2.60 tff(3,plain,
% 2.44/2.60 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(4,plain,
% 2.44/2.60 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 2.44/2.60 inference(bind,[status(th)],[])).
% 2.44/2.60 tff(5,plain,
% 2.44/2.60 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(quant_intro,[status(thm)],[4])).
% 2.44/2.60 tff(6,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 2.44/2.60 tff(7,plain,
% 2.44/2.60 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.44/2.60 tff(8,plain,
% 2.44/2.60 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.44/2.60 tff(9,plain,(
% 2.44/2.60 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(skolemize,[status(sab)],[8])).
% 2.44/2.60 tff(10,plain,
% 2.44/2.60 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.44/2.61 tff(11,plain,
% 2.44/2.61 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12,plain,
% 2.44/2.61 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(13,plain,
% 2.44/2.61 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12])).
% 2.44/2.61 tff(14,plain,
% 2.44/2.61 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[13, 11])).
% 2.44/2.61 tff(15,plain,
% 2.44/2.61 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C)))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(16,plain,
% 2.44/2.61 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C)))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(17,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_tsp_2')).
% 2.44/2.61 tff(18,plain,
% 2.44/2.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[17, 16])).
% 2.44/2.61 tff(19,plain,
% 2.44/2.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[18, 15])).
% 2.44/2.61 tff(20,plain,
% 2.44/2.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[19, 15])).
% 2.44/2.61 tff(21,plain,
% 2.44/2.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(A, C)) = k4_pre_topc(A, B, k3_tsp_2(A, B), k4_tex_4(A, C))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[20, 15])).
% 2.44/2.61 tff(22,plain,
% 2.44/2.61 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[21, 14])).
% 2.44/2.61 tff(23,plain,
% 2.44/2.61 (l1_pre_topc(A!0)),
% 2.44/2.61 inference(and_elim,[status(thm)],[22])).
% 2.44/2.61 tff(24,plain,
% 2.44/2.61 (((~![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)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(25,plain,
% 2.44/2.61 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(26,plain,
% 2.44/2.61 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.44/2.61 tff(27,plain,
% 2.44/2.61 (l1_struct_0(A!0)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 2.44/2.61 tff(28,plain,
% 2.44/2.61 (^[A: $i] : refl(((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(29,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[28])).
% 2.44/2.61 tff(30,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(31,plain,
% 2.44/2.61 (^[A: $i] : rewrite((l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A))) <=> ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(32,plain,
% 2.44/2.61 (![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A))) <=> ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[31])).
% 2.44/2.61 tff(33,axiom,(![A: $i] : (l1_struct_0(A) => (k2_pre_topc(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_pre_topc')).
% 2.44/2.61 tff(34,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.44/2.61 tff(35,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[34, 30])).
% 2.44/2.61 tff(36,plain,(
% 2.44/2.61 ![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(skolemize,[status(sab)],[35])).
% 2.44/2.61 tff(37,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[36, 29])).
% 2.44/2.61 tff(38,plain,
% 2.44/2.61 (((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | (~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(39,plain,
% 2.44/2.61 ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | ((~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(40,plain,
% 2.44/2.61 ((~![A: $i] : ((~l1_struct_0(A)) | (k2_pre_topc(A) = u1_struct_0(A)))) | (~l1_struct_0(A!0)) | (k2_pre_topc(A!0) = u1_struct_0(A!0))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.44/2.61 tff(41,plain,
% 2.44/2.61 (k2_pre_topc(A!0) = u1_struct_0(A!0)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 2.44/2.61 tff(42,plain,
% 2.44/2.61 (^[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)))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(43,plain,
% 2.44/2.61 (![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))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[42])).
% 2.44/2.61 tff(44,plain,
% 2.44/2.61 (^[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)))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(45,plain,
% 2.44/2.61 (![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))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[44])).
% 2.44/2.61 tff(46,plain,
% 2.44/2.61 (![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))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[45, 43])).
% 2.44/2.61 tff(47,plain,
% 2.44/2.61 (![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))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(48,plain,
% 2.44/2.61 (^[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))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(49,plain,
% 2.44/2.61 (![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))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[48])).
% 2.44/2.61 tff(50,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')).
% 2.44/2.61 tff(51,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[50, 49])).
% 2.44/2.61 tff(52,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[51, 47])).
% 2.44/2.61 tff(53,plain,(
% 2.44/2.61 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 2.44/2.61 inference(skolemize,[status(sab)],[52])).
% 2.44/2.61 tff(54,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[53, 46])).
% 2.44/2.61 tff(55,plain,
% 2.44/2.61 (((~![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))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(56,plain,
% 2.44/2.61 ((~![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))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(57,plain,
% 2.44/2.61 ((~![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)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.44/2.61 tff(58,plain,
% 2.44/2.61 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[57, 23, 54])).
% 2.44/2.61 tff(59,plain,
% 2.44/2.61 (m2_tsp_1(B!1, A!0)),
% 2.44/2.61 inference(and_elim,[status(thm)],[22])).
% 2.44/2.61 tff(60,plain,
% 2.44/2.61 (((~![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)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(61,plain,
% 2.44/2.61 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(62,plain,
% 2.44/2.61 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[61, 60])).
% 2.44/2.61 tff(63,plain,
% 2.44/2.61 (l1_pre_topc(B!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[62, 59, 58])).
% 2.44/2.61 tff(64,plain,
% 2.44/2.61 (((~![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)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(65,plain,
% 2.44/2.61 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(66,plain,
% 2.44/2.61 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.44/2.61 tff(67,plain,
% 2.44/2.61 (l1_struct_0(B!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[66, 10, 63])).
% 2.44/2.61 tff(68,plain,
% 2.44/2.61 (^[A: $i] : refl(((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(69,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[68])).
% 2.44/2.61 tff(70,plain,
% 2.44/2.61 (^[A: $i] : rewrite(((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(71,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[70])).
% 2.44/2.61 tff(72,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[71, 69])).
% 2.44/2.61 tff(73,plain,
% 2.44/2.61 (^[A: $i] : rewrite(((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(74,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[73])).
% 2.44/2.61 tff(75,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(76,plain,
% 2.44/2.61 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(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)) & 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))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))), ((((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> (((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), rewrite((((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))), ((((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))), (![B: $i] : (((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), ((l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> (l1_struct_0(A) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))), rewrite((l1_struct_0(A) => ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), ((l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(77,plain,
% 2.44/2.61 (![A: $i] : (l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[76])).
% 2.44/2.61 tff(78,axiom,(![A: $i] : (l1_struct_0(A) => ![B: $i] : (((~v3_struct_0(B)) & l1_struct_0(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t51_tops_2')).
% 2.44/2.61 tff(79,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[78, 77])).
% 2.44/2.61 tff(80,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[79, 75])).
% 2.44/2.61 tff(81,plain,(
% 2.44/2.61 ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_struct_0(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((k1_relat_1(C) = k2_pre_topc(A)) & r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))),
% 2.44/2.61 inference(skolemize,[status(sab)],[80])).
% 2.44/2.61 tff(82,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[81, 74])).
% 2.44/2.61 tff(83,plain,
% 2.44/2.61 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[82, 72])).
% 2.44/2.61 tff(84,plain,
% 2.44/2.61 (((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | (~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(85,plain,
% 2.44/2.61 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(86,plain,
% 2.44/2.61 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B))))))))) | (~l1_struct_0(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[85, 84])).
% 2.44/2.61 tff(87,plain,
% 2.44/2.61 (![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[86, 83, 27])).
% 2.44/2.61 tff(88,plain,
% 2.44/2.61 (~v3_struct_0(B!1)),
% 2.44/2.61 inference(and_elim,[status(thm)],[22])).
% 2.44/2.61 tff(89,plain,
% 2.44/2.61 (((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1)))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1)))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(90,plain,
% 2.44/2.61 ((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | (v3_struct_0(B!1) | (~l1_struct_0(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1)))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(91,plain,
% 2.44/2.61 ((~![B: $i] : (v3_struct_0(B) | (~l1_struct_0(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B)))))))) | v3_struct_0(B!1) | (~l1_struct_0(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.44/2.61 tff(92,plain,
% 2.44/2.61 ((~l1_struct_0(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[91, 88, 87])).
% 2.44/2.61 tff(93,plain,
% 2.44/2.61 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[92, 67])).
% 2.44/2.61 tff(94,plain,
% 2.44/2.61 (^[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))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(95,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[94])).
% 2.44/2.61 tff(96,plain,
% 2.44/2.61 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(97,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[96])).
% 2.44/2.61 tff(98,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(transitivity,[status(thm)],[97, 95])).
% 2.44/2.61 tff(99,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(100,plain,
% 2.44/2.61 (^[A: $i] : rewrite((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(101,plain,
% 2.44/2.61 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[100])).
% 2.44/2.61 tff(102,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')).
% 2.44/2.61 tff(103,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[102, 101])).
% 2.44/2.61 tff(104,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[103, 99])).
% 2.44/2.61 tff(105,plain,(
% 2.44/2.61 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(skolemize,[status(sab)],[104])).
% 2.44/2.61 tff(106,plain,
% 2.44/2.61 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[105, 98])).
% 2.44/2.61 tff(107,plain,
% 2.44/2.61 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(108,plain,
% 2.44/2.61 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(109,plain,
% 2.44/2.61 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[108, 107])).
% 2.44/2.61 tff(110,plain,
% 2.44/2.61 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[109, 23, 106])).
% 2.44/2.61 tff(111,plain,
% 2.44/2.61 ((~![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))) | (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(112,plain,
% 2.44/2.61 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[111, 110])).
% 2.44/2.61 tff(113,plain,
% 2.44/2.61 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | (~m2_tsp_1(B!1, A!0)) | m1_pre_topc(B!1, A!0)),
% 2.44/2.61 inference(tautology,[status(thm)],[])).
% 2.44/2.61 tff(114,plain,
% 2.44/2.61 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[113, 59])).
% 2.44/2.61 tff(115,plain,
% 2.44/2.61 (m1_pre_topc(B!1, A!0)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[114, 112])).
% 2.44/2.61 tff(116,plain,
% 2.44/2.61 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(117,plain,
% 2.44/2.61 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[116])).
% 2.44/2.61 tff(118,plain,
% 2.44/2.61 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(119,plain,
% 2.44/2.61 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[118])).
% 2.44/2.61 tff(120,plain,
% 2.44/2.61 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(121,plain,
% 2.44/2.61 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), trans(monotonicity(rewrite(((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B))), ((((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(122,plain,
% 2.44/2.61 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[121])).
% 2.44/2.61 tff(123,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tsp_2')).
% 2.44/2.61 tff(124,plain,
% 2.44/2.61 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[123, 122])).
% 2.44/2.62 tff(125,plain,
% 2.44/2.62 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[124, 120])).
% 2.44/2.62 tff(126,plain,(
% 2.44/2.62 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.44/2.62 inference(skolemize,[status(sab)],[125])).
% 2.44/2.62 tff(127,plain,
% 2.44/2.62 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[126, 119])).
% 2.44/2.62 tff(128,plain,
% 2.44/2.62 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[127, 117])).
% 2.44/2.62 tff(129,plain,
% 2.44/2.62 (v2_tsp_2(B!1, A!0)),
% 2.44/2.62 inference(and_elim,[status(thm)],[22])).
% 2.44/2.62 tff(130,plain,
% 2.44/2.62 (v2_pre_topc(A!0)),
% 2.44/2.62 inference(and_elim,[status(thm)],[22])).
% 2.44/2.62 tff(131,plain,
% 2.44/2.62 (~v3_struct_0(A!0)),
% 2.44/2.62 inference(and_elim,[status(thm)],[22])).
% 2.44/2.62 tff(132,plain,
% 2.44/2.62 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(133,plain,
% 2.44/2.62 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(134,plain,
% 2.44/2.62 ((~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(135,plain,
% 2.44/2.62 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[134])).
% 2.44/2.62 tff(136,plain,
% 2.44/2.62 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[135, 133])).
% 2.44/2.62 tff(137,plain,
% 2.44/2.62 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[136])).
% 2.44/2.62 tff(138,plain,
% 2.44/2.62 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[137, 132])).
% 2.44/2.62 tff(139,plain,
% 2.44/2.62 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(140,plain,
% 2.44/2.62 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[139, 138])).
% 2.44/2.62 tff(141,plain,
% 2.44/2.62 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[140, 131, 130, 23, 88, 129, 128])).
% 2.44/2.62 tff(142,plain,
% 2.44/2.62 (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[141, 115])).
% 2.44/2.62 tff(143,plain,
% 2.44/2.62 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.62 inference(tautology,[status(thm)],[])).
% 2.44/2.62 tff(144,plain,
% 2.44/2.62 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[143, 142])).
% 2.44/2.62 tff(145,plain,
% 2.44/2.62 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.62 inference(tautology,[status(thm)],[])).
% 2.44/2.62 tff(146,plain,
% 2.44/2.62 (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[145, 142])).
% 2.44/2.62 tff(147,plain,
% 2.44/2.62 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k1_tsp_2(A!0, B!1))),
% 2.44/2.62 inference(tautology,[status(thm)],[])).
% 2.44/2.62 tff(148,plain,
% 2.44/2.62 (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[147, 142])).
% 2.44/2.62 tff(149,plain,
% 2.44/2.62 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(150,plain,
% 2.44/2.62 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(151,plain,
% 2.44/2.62 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(C) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(C), k2_pre_topc(B!1))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.44/2.62 tff(152,plain,
% 2.44/2.62 (~((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[151, 148, 146, 144, 93])).
% 2.44/2.62 tff(153,plain,
% 2.44/2.62 (((~(k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))) | (~r1_tarski(k2_relat_1(k1_tsp_2(A!0, B!1)), k2_pre_topc(B!1)))) | (k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0))),
% 2.44/2.62 inference(tautology,[status(thm)],[])).
% 2.44/2.62 tff(154,plain,
% 2.44/2.62 (k1_relat_1(k1_tsp_2(A!0, B!1)) = k2_pre_topc(A!0)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[153, 152])).
% 2.44/2.62 tff(155,plain,
% 2.44/2.62 (k1_relat_1(k1_tsp_2(A!0, B!1)) = u1_struct_0(A!0)),
% 2.44/2.62 inference(transitivity,[status(thm)],[154, 41])).
% 2.44/2.62 tff(156,plain,
% 2.44/2.62 (r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[155])).
% 2.44/2.62 tff(157,plain,
% 2.44/2.62 (r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)) <=> r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 2.44/2.62 inference(symmetry,[status(thm)],[156])).
% 2.44/2.62 tff(158,plain,
% 2.44/2.62 (^[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)))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(159,plain,
% 2.44/2.62 (![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))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[158])).
% 2.44/2.62 tff(160,plain,
% 2.44/2.62 (![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))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(161,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')).
% 2.44/2.62 tff(162,plain,
% 2.44/2.62 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.44/2.62 tff(163,plain,(
% 2.44/2.62 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 2.44/2.62 inference(skolemize,[status(sab)],[162])).
% 2.44/2.62 tff(164,plain,
% 2.44/2.62 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[163, 159])).
% 2.44/2.62 tff(165,plain,
% 2.44/2.62 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(166,plain,
% 2.44/2.62 (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[165, 164])).
% 2.44/2.62 tff(167,plain,
% 2.44/2.62 (^[A: $i, B: $i] : refl((m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A))) <=> (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(168,plain,
% 2.44/2.62 (![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[167])).
% 2.44/2.62 tff(169,plain,
% 2.44/2.62 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~l1_pre_topc(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))), (((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(170,plain,
% 2.44/2.62 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[169])).
% 2.44/2.62 tff(171,plain,
% 2.44/2.62 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(172,plain,
% 2.44/2.62 (^[A: $i, B: $i] : rewrite(((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(173,plain,
% 2.44/2.62 (![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[172])).
% 2.44/2.62 tff(174,axiom,(![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_tex_4')).
% 2.44/2.62 tff(175,plain,
% 2.44/2.62 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[174, 173])).
% 2.44/2.62 tff(176,plain,
% 2.44/2.62 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[175, 171])).
% 2.44/2.62 tff(177,plain,(
% 2.44/2.62 ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 2.44/2.62 inference(skolemize,[status(sab)],[176])).
% 2.44/2.62 tff(178,plain,
% 2.44/2.62 (![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[177, 170])).
% 2.44/2.62 tff(179,plain,
% 2.44/2.62 (![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[178, 168])).
% 2.44/2.62 tff(180,plain,
% 2.44/2.62 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 2.44/2.62 inference(and_elim,[status(thm)],[22])).
% 2.44/2.62 tff(181,plain,
% 2.44/2.62 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 2.44/2.62 inference(or_elim,[status(thm)],[180])).
% 2.44/2.62 tff(182,plain,
% 2.44/2.62 (((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(183,plain,
% 2.44/2.62 ((m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(184,plain,
% 2.44/2.62 (((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[183])).
% 2.44/2.62 tff(185,plain,
% 2.44/2.62 (((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[184, 182])).
% 2.44/2.62 tff(186,plain,
% 2.44/2.62 ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(187,plain,
% 2.44/2.62 ((~![A: $i, B: $i] : (m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_pre_topc(A!0)) | m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[186, 185])).
% 2.44/2.62 tff(188,plain,
% 2.44/2.62 (m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[187, 23, 181, 179])).
% 2.44/2.62 tff(189,plain,
% 2.44/2.62 ((~(m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)))) | (~m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 2.44/2.62 inference(tautology,[status(thm)],[])).
% 2.44/2.62 tff(190,plain,
% 2.44/2.62 ((~(m1_subset_1(k2_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0)))) | r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[189, 188])).
% 2.44/2.62 tff(191,plain,
% 2.44/2.62 (r1_tarski(k2_tex_4(A!0, C!2), u1_struct_0(A!0))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[190, 166])).
% 2.44/2.62 tff(192,plain,
% 2.44/2.62 (r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[191, 157])).
% 2.44/2.62 tff(193,plain,
% 2.44/2.62 (^[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))) | (~v2_pre_topc(A)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(194,plain,
% 2.44/2.62 (![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))) | (~v2_pre_topc(A)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[193])).
% 2.44/2.62 tff(195,plain,
% 2.44/2.62 (^[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))) | (~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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_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) | (~m1_subset_1(B, u1_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)))) | (k4_tex_4(A, B) = k2_tex_4(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_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))) | (~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)))) | (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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(196,plain,
% 2.44/2.62 (![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[195])).
% 2.44/2.62 tff(197,plain,
% 2.44/2.62 (![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)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(198,plain,
% 2.44/2.62 (^[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)))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(199,plain,
% 2.44/2.62 (![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)))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[198])).
% 2.44/2.62 tff(200,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')).
% 2.44/2.62 tff(201,plain,
% 2.44/2.62 (![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)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[200, 199])).
% 2.44/2.62 tff(202,plain,
% 2.44/2.62 (![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)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[201, 197])).
% 2.44/2.62 tff(203,plain,(
% 2.44/2.62 ![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)))),
% 2.44/2.62 inference(skolemize,[status(sab)],[202])).
% 2.44/2.62 tff(204,plain,
% 2.44/2.62 (![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[203, 196])).
% 2.44/2.62 tff(205,plain,
% 2.44/2.62 (![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[204, 194])).
% 2.44/2.62 tff(206,plain,
% 2.44/2.62 (((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))) <=> ((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(207,plain,
% 2.44/2.62 ((v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(208,plain,
% 2.44/2.62 (((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[207])).
% 2.44/2.62 tff(209,plain,
% 2.44/2.62 (((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[208, 206])).
% 2.44/2.62 tff(210,plain,
% 2.44/2.62 ((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(211,plain,
% 2.44/2.62 ((~![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))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.44/2.62 tff(212,plain,
% 2.44/2.62 (k4_tex_4(A!0, C!2) = k2_tex_4(A!0, C!2)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[211, 131, 130, 23, 181, 205])).
% 2.44/2.62 tff(213,plain,
% 2.44/2.62 (k2_tex_4(A!0, C!2) = k4_tex_4(A!0, C!2)),
% 2.44/2.62 inference(symmetry,[status(thm)],[212])).
% 2.44/2.62 tff(214,plain,
% 2.44/2.62 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(215,plain,
% 2.44/2.63 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[214])).
% 2.44/2.63 tff(216,plain,
% 2.44/2.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(217,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[216])).
% 2.44/2.63 tff(218,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(219,plain,
% 2.44/2.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(220,plain,
% 2.44/2.63 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[219])).
% 2.44/2.63 tff(221,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k3_tsp_2(A, B) = k1_tsp_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_tsp_2')).
% 2.44/2.63 tff(222,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[221, 220])).
% 2.44/2.63 tff(223,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[222, 218])).
% 2.44/2.63 tff(224,plain,(
% 2.44/2.63 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 2.44/2.63 inference(skolemize,[status(sab)],[223])).
% 2.44/2.63 tff(225,plain,
% 2.44/2.63 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[224, 217])).
% 2.44/2.63 tff(226,plain,
% 2.44/2.63 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[225, 215])).
% 2.44/2.63 tff(227,plain,
% 2.44/2.63 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(228,plain,
% 2.44/2.63 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(229,plain,
% 2.44/2.63 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[228])).
% 2.44/2.63 tff(230,plain,
% 2.44/2.63 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[229, 227])).
% 2.44/2.63 tff(231,plain,
% 2.44/2.63 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(232,plain,
% 2.44/2.63 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k3_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[231, 230])).
% 2.44/2.63 tff(233,plain,
% 2.44/2.63 ((k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[232, 131, 130, 23, 88, 129, 226])).
% 2.44/2.63 tff(234,plain,
% 2.44/2.63 (k3_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[233, 115])).
% 2.44/2.63 tff(235,plain,
% 2.44/2.63 (k1_tsp_2(A!0, B!1) = k3_tsp_2(A!0, B!1)),
% 2.44/2.63 inference(symmetry,[status(thm)],[234])).
% 2.44/2.63 tff(236,plain,
% 2.44/2.63 (k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[235, 213])).
% 2.44/2.63 tff(237,plain,
% 2.44/2.63 (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2))),
% 2.44/2.63 inference(symmetry,[status(thm)],[236])).
% 2.44/2.63 tff(238,plain,
% 2.44/2.63 ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) <=> (k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[237])).
% 2.44/2.63 tff(239,plain,
% 2.44/2.63 (^[A: $i, B: $i] : refl((r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))) <=> (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(240,plain,
% 2.44/2.63 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))) <=> ![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[239])).
% 2.44/2.63 tff(241,plain,
% 2.44/2.63 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B)))) <=> ![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(242,axiom,(![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t39_zfmisc_1')).
% 2.44/2.63 tff(243,plain,
% 2.44/2.63 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[242, 241])).
% 2.44/2.63 tff(244,plain,(
% 2.44/2.63 ![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 2.44/2.63 inference(skolemize,[status(sab)],[243])).
% 2.44/2.63 tff(245,plain,
% 2.44/2.63 (![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[244, 240])).
% 2.44/2.63 tff(246,plain,
% 2.44/2.63 ((~![A: $i, B: $i] : (r1_tarski(A, k1_tarski(B)) <=> ((A = k1_xboole_0) | (A = k1_tarski(B))))) | (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(247,plain,
% 2.44/2.63 (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[246, 245])).
% 2.44/2.63 tff(248,plain,
% 2.44/2.63 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[234])).
% 2.44/2.63 tff(249,plain,
% 2.44/2.63 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) <=> m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[248])).
% 2.44/2.63 tff(250,plain,
% 2.44/2.63 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) <=> m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 2.44/2.63 inference(symmetry,[status(thm)],[249])).
% 2.44/2.63 tff(251,plain,
% 2.44/2.63 (^[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)))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(252,plain,
% 2.44/2.63 (![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))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[251])).
% 2.44/2.63 tff(253,plain,
% 2.44/2.63 (![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))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(254,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')).
% 2.44/2.63 tff(255,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[254, 253])).
% 2.44/2.63 tff(256,plain,(
% 2.44/2.63 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.63 inference(skolemize,[status(sab)],[255])).
% 2.44/2.63 tff(257,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[256, 252])).
% 2.44/2.63 tff(258,plain,
% 2.44/2.63 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(259,plain,
% 2.44/2.63 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[258, 257])).
% 2.44/2.63 tff(260,plain,
% 2.44/2.63 ((~(m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.63 inference(tautology,[status(thm)],[])).
% 2.44/2.63 tff(261,plain,
% 2.44/2.63 ((~(m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[260, 144])).
% 2.44/2.63 tff(262,plain,
% 2.44/2.63 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[261, 259])).
% 2.44/2.63 tff(263,plain,
% 2.44/2.63 (^[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))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(264,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[263])).
% 2.44/2.63 tff(265,plain,
% 2.44/2.63 (^[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)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(266,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[265])).
% 2.44/2.63 tff(267,plain,
% 2.44/2.63 (![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))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(268,plain,
% 2.44/2.63 (^[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)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(269,plain,
% 2.44/2.63 (![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))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[268])).
% 2.44/2.63 tff(270,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')).
% 2.44/2.63 tff(271,plain,
% 2.44/2.63 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[270, 269])).
% 2.44/2.63 tff(272,plain,
% 2.44/2.63 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[271, 267])).
% 2.44/2.63 tff(273,plain,(
% 2.44/2.63 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.44/2.63 inference(skolemize,[status(sab)],[272])).
% 2.44/2.63 tff(274,plain,
% 2.44/2.63 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[273, 266])).
% 2.44/2.63 tff(275,plain,
% 2.44/2.63 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[274, 264])).
% 2.44/2.63 tff(276,plain,
% 2.44/2.63 (((~![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))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(277,plain,
% 2.44/2.63 ((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))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(278,plain,
% 2.44/2.63 (((~![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)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[277])).
% 2.44/2.63 tff(279,plain,
% 2.44/2.63 (((~![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))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[278, 276])).
% 2.44/2.63 tff(280,plain,
% 2.44/2.63 ((~![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)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(281,plain,
% 2.44/2.63 ((~![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)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[280, 279])).
% 2.44/2.63 tff(282,plain,
% 2.44/2.63 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[281, 131, 275])).
% 2.44/2.63 tff(283,plain,
% 2.44/2.63 (~v1_xboole_0(u1_struct_0(A!0))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[282, 27])).
% 2.44/2.63 tff(284,plain,
% 2.44/2.63 (^[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))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(285,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[284])).
% 2.44/2.63 tff(286,plain,
% 2.44/2.63 (^[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)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(287,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[286])).
% 2.44/2.63 tff(288,plain,
% 2.44/2.63 (![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))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(289,plain,
% 2.44/2.63 (^[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))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(290,plain,
% 2.44/2.63 (![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))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[289])).
% 2.44/2.63 tff(291,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')).
% 2.44/2.63 tff(292,plain,
% 2.44/2.63 (![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))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[291, 290])).
% 2.44/2.63 tff(293,plain,
% 2.44/2.63 (![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))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[292, 288])).
% 2.44/2.63 tff(294,plain,(
% 2.44/2.63 ![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))),
% 2.44/2.63 inference(skolemize,[status(sab)],[293])).
% 2.44/2.63 tff(295,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[294, 287])).
% 2.44/2.63 tff(296,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[295, 285])).
% 2.44/2.63 tff(297,plain,
% 2.44/2.63 (((~![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(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), 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), k1_tsp_2(A!0, B!1), C!2), 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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), 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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(298,plain,
% 2.44/2.63 ((m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), 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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(299,plain,
% 2.44/2.63 (((~![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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), 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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[298])).
% 2.44/2.63 tff(300,plain,
% 2.44/2.63 (((~![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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), 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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[299, 297])).
% 2.44/2.63 tff(301,plain,
% 2.44/2.63 ((~![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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(302,plain,
% 2.44/2.63 ((~![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(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), 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), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[301, 300])).
% 2.44/2.63 tff(303,plain,
% 2.44/2.63 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[302, 181, 296, 283, 148, 146, 262])).
% 2.44/2.63 tff(304,plain,
% 2.44/2.63 (m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[303, 250])).
% 2.44/2.63 tff(305,plain,
% 2.44/2.63 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(306,plain,
% 2.44/2.63 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[305])).
% 2.44/2.63 tff(307,plain,
% 2.44/2.63 (^[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)) | (~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) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(308,plain,
% 2.44/2.63 (![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)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[307])).
% 2.44/2.63 tff(309,plain,
% 2.44/2.63 (![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)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(310,plain,
% 2.44/2.63 (^[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)))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(311,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[310])).
% 2.44/2.64 tff(312,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')).
% 2.44/2.64 tff(313,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[312, 311])).
% 2.44/2.64 tff(314,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[313, 309])).
% 2.44/2.64 tff(315,plain,(
% 2.44/2.64 ![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)))),
% 2.44/2.64 inference(skolemize,[status(sab)],[314])).
% 2.44/2.64 tff(316,plain,
% 2.44/2.64 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[315, 308])).
% 2.44/2.64 tff(317,plain,
% 2.44/2.64 (![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[316, 306])).
% 2.44/2.64 tff(318,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(319,plain,
% 2.44/2.64 ((v3_struct_0(B!1) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(320,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[319])).
% 2.44/2.64 tff(321,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[320, 318])).
% 2.44/2.64 tff(322,plain,
% 2.44/2.64 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~l1_struct_0(B!1)) | (~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(323,plain,
% 2.44/2.64 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_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), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[322, 321])).
% 2.44/2.64 tff(324,plain,
% 2.44/2.64 ((~m1_subset_1(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2), u1_struct_0(B!1))) | (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[323, 88, 317, 67])).
% 2.44/2.64 tff(325,plain,
% 2.44/2.64 (k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[324, 304])).
% 2.44/2.64 tff(326,plain,
% 2.44/2.64 (k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 2.44/2.64 inference(symmetry,[status(thm)],[325])).
% 2.44/2.64 tff(327,plain,
% 2.44/2.64 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)),
% 2.44/2.64 inference(symmetry,[status(thm)],[248])).
% 2.44/2.64 tff(328,plain,
% 2.44/2.64 (^[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))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(329,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[328])).
% 2.44/2.64 tff(330,plain,
% 2.44/2.64 (^[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)))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(331,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[330])).
% 2.44/2.64 tff(332,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(333,plain,
% 2.44/2.64 (^[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)))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(334,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[333])).
% 2.44/2.64 tff(335,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')).
% 2.44/2.64 tff(336,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[335, 334])).
% 2.44/2.64 tff(337,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[336, 332])).
% 2.44/2.64 tff(338,plain,(
% 2.44/2.64 ![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)))),
% 2.44/2.64 inference(skolemize,[status(sab)],[337])).
% 2.44/2.64 tff(339,plain,
% 2.44/2.64 (![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)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[338, 331])).
% 2.44/2.64 tff(340,plain,
% 2.44/2.64 (![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)))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[339, 329])).
% 2.49/2.64 tff(341,plain,
% 2.49/2.64 (((~![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)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))) <=> ((~![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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.64 inference(rewrite,[status(thm)],[])).
% 2.49/2.64 tff(342,plain,
% 2.49/2.64 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.64 inference(rewrite,[status(thm)],[])).
% 2.49/2.64 tff(343,plain,
% 2.49/2.64 (((~![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), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[342])).
% 2.49/2.64 tff(344,plain,
% 2.49/2.64 (((~![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), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, 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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.64 inference(transitivity,[status(thm)],[343, 341])).
% 2.49/2.64 tff(345,plain,
% 2.49/2.64 ((~![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), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 2.49/2.64 inference(quant_inst,[status(thm)],[])).
% 2.49/2.64 tff(346,plain,
% 2.49/2.64 ((~![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)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[345, 344])).
% 2.49/2.64 tff(347,plain,
% 2.49/2.64 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2) = k1_funct_1(k1_tsp_2(A!0, B!1), C!2)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[346, 181, 340, 283, 148, 146, 262])).
% 2.49/2.64 tff(348,plain,
% 2.49/2.64 (k1_funct_1(k1_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k1_tsp_2(A!0, B!1), C!2)),
% 2.49/2.64 inference(symmetry,[status(thm)],[347])).
% 2.49/2.64 tff(349,plain,
% 2.49/2.64 (k1_funct_1(k1_tsp_2(A!0, B!1), C!2) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)),
% 2.49/2.64 inference(transitivity,[status(thm)],[348, 327])).
% 2.49/2.64 tff(350,plain,
% 2.49/2.64 (k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k1_tarski(k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[349])).
% 2.49/2.64 tff(351,plain,
% 2.49/2.64 (k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))),
% 2.49/2.64 inference(transitivity,[status(thm)],[350, 326])).
% 2.49/2.64 tff(352,plain,
% 2.49/2.64 (^[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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))),
% 2.49/2.64 inference(bind,[status(th)],[])).
% 2.49/2.64 tff(353,plain,
% 2.49/2.64 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(quant_intro,[status(thm)],[352])).
% 2.49/2.64 tff(354,plain,
% 2.49/2.64 (^[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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))),
% 2.49/2.64 inference(bind,[status(th)],[])).
% 2.49/2.64 tff(355,plain,
% 2.49/2.64 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(quant_intro,[status(thm)],[354])).
% 2.49/2.64 tff(356,plain,
% 2.49/2.64 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(transitivity,[status(thm)],[355, 353])).
% 2.49/2.64 tff(357,plain,
% 2.49/2.64 (^[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))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ((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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), 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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))))),
% 2.49/2.64 inference(bind,[status(th)],[])).
% 2.49/2.64 tff(358,plain,
% 2.49/2.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(quant_intro,[status(thm)],[357])).
% 2.49/2.64 tff(359,plain,
% 2.49/2.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(rewrite,[status(thm)],[])).
% 2.49/2.64 tff(360,plain,
% 2.49/2.64 (^[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] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))))), 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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))))),
% 2.49/2.64 inference(bind,[status(th)],[])).
% 2.49/2.64 tff(361,plain,
% 2.49/2.64 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(quant_intro,[status(thm)],[360])).
% 2.49/2.64 tff(362,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_tsp_2')).
% 2.49/2.64 tff(363,plain,
% 2.49/2.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[362, 361])).
% 2.49/2.64 tff(364,plain,
% 2.49/2.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[363, 359])).
% 2.49/2.64 tff(365,plain,(
% 2.49/2.64 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.64 inference(skolemize,[status(sab)],[364])).
% 2.49/2.64 tff(366,plain,
% 2.49/2.64 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[365, 358])).
% 2.49/2.65 tff(367,plain,
% 2.49/2.65 (![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[366, 356])).
% 2.49/2.65 tff(368,plain,
% 2.49/2.65 (((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0))))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(369,plain,
% 2.49/2.65 ((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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0))))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(370,plain,
% 2.49/2.65 (((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C)))))) <=> ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[369])).
% 2.49/2.65 tff(371,plain,
% 2.49/2.65 (((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C)))))) <=> ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0))))),
% 2.49/2.65 inference(transitivity,[status(thm)],[370, 368])).
% 2.49/2.65 tff(372,plain,
% 2.49/2.65 ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | (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] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C)))))),
% 2.49/2.65 inference(quant_inst,[status(thm)],[])).
% 2.49/2.65 tff(373,plain,
% 2.49/2.65 ((~![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] : ((~m1_subset_1(C, u1_struct_0(A))) | (k5_pre_topc(A, B, k3_tsp_2(A, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A), u1_struct_0(B), k3_tsp_2(A, B), C))) = k4_tex_4(A, C)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[372, 371])).
% 2.49/2.65 tff(374,plain,
% 2.49/2.65 (![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[373, 131, 130, 23, 367])).
% 2.49/2.65 tff(375,plain,
% 2.49/2.65 (((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))) <=> ((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(376,plain,
% 2.49/2.65 ((v3_struct_0(B!1) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(377,plain,
% 2.49/2.65 (((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | (v3_struct_0(B!1) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)))) <=> ((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[376])).
% 2.49/2.65 tff(378,plain,
% 2.49/2.65 (((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | (v3_struct_0(B!1) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)))) <=> ((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))))),
% 2.49/2.65 inference(transitivity,[status(thm)],[377, 375])).
% 2.49/2.65 tff(379,plain,
% 2.49/2.65 ((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | (v3_struct_0(B!1) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)))),
% 2.49/2.65 inference(quant_inst,[status(thm)],[])).
% 2.49/2.65 tff(380,plain,
% 2.49/2.65 ((~![B: $i] : (v3_struct_0(B) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B, k3_tsp_2(A!0, B), k1_struct_0(B, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B), k3_tsp_2(A!0, B), C))) = k4_tex_4(A!0, C))) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)))) | v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | (~m2_tsp_1(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[379, 378])).
% 2.49/2.65 tff(381,plain,
% 2.49/2.65 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[380, 88, 129, 59, 374])).
% 2.49/2.65 tff(382,plain,
% 2.49/2.65 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(383,plain,
% 2.49/2.65 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)))),
% 2.49/2.65 inference(quant_inst,[status(thm)],[])).
% 2.49/2.65 tff(384,plain,
% 2.49/2.65 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C))) = k4_tex_4(A!0, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[383, 382])).
% 2.49/2.65 tff(385,plain,
% 2.49/2.65 (k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[384, 181, 381])).
% 2.49/2.65 tff(386,plain,
% 2.49/2.65 (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k5_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[235])).
% 2.49/2.65 tff(387,plain,
% 2.49/2.65 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))),
% 2.49/2.65 inference(bind,[status(th)],[])).
% 2.49/2.65 tff(388,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.65 inference(quant_intro,[status(thm)],[387])).
% 2.49/2.65 tff(389,plain,
% 2.49/2.65 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> (((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))))), rewrite((((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.65 inference(bind,[status(th)],[])).
% 2.49/2.65 tff(390,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.65 inference(quant_intro,[status(thm)],[389])).
% 2.49/2.65 tff(391,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(392,plain,
% 2.49/2.65 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))))),
% 2.49/2.65 inference(bind,[status(th)],[])).
% 2.49/2.65 tff(393,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.49/2.65 inference(quant_intro,[status(thm)],[392])).
% 2.49/2.65 tff(394,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_pre_topc')).
% 2.49/2.65 tff(395,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[394, 393])).
% 2.49/2.65 tff(396,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[395, 391])).
% 2.49/2.65 tff(397,plain,(
% 2.49/2.65 ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.49/2.65 inference(skolemize,[status(sab)],[396])).
% 2.49/2.65 tff(398,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[397, 390])).
% 2.49/2.65 tff(399,plain,
% 2.49/2.65 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[398, 388])).
% 2.49/2.65 tff(400,plain,
% 2.49/2.65 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(401,plain,
% 2.49/2.65 (((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 2.49/2.65 inference(rewrite,[status(thm)],[])).
% 2.49/2.65 tff(402,plain,
% 2.49/2.65 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[401])).
% 2.49/2.65 tff(403,plain,
% 2.49/2.65 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))))),
% 2.49/2.65 inference(transitivity,[status(thm)],[402, 400])).
% 2.49/2.65 tff(404,plain,
% 2.49/2.65 ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.49/2.65 inference(quant_inst,[status(thm)],[])).
% 2.49/2.65 tff(405,plain,
% 2.49/2.65 ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[404, 403])).
% 2.49/2.66 tff(406,plain,
% 2.49/2.66 (k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(unit_resolution,[status(thm)],[405, 399, 27, 67, 148, 146, 262])).
% 2.49/2.66 tff(407,plain,
% 2.49/2.66 (k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k5_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(symmetry,[status(thm)],[406])).
% 2.49/2.66 tff(408,plain,
% 2.49/2.66 (k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) = k4_tex_4(A!0, C!2)),
% 2.49/2.66 inference(transitivity,[status(thm)],[407, 386, 385])).
% 2.49/2.66 tff(409,plain,
% 2.49/2.66 (k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))),
% 2.49/2.66 inference(monotonicity,[status(thm)],[235, 408])).
% 2.49/2.66 tff(410,plain,
% 2.49/2.66 (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))))),
% 2.49/2.66 inference(symmetry,[status(thm)],[409])).
% 2.49/2.66 tff(411,plain,
% 2.49/2.66 (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(monotonicity,[status(thm)],[410, 351])).
% 2.49/2.66 tff(412,plain,
% 2.49/2.66 (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) <=> r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(symmetry,[status(thm)],[411])).
% 2.49/2.66 tff(413,plain,
% 2.49/2.66 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(414,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[413])).
% 2.49/2.66 tff(415,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(416,plain,
% 2.49/2.66 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(417,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[416])).
% 2.49/2.66 tff(418,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 2.49/2.66 tff(419,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[418, 417])).
% 2.49/2.66 tff(420,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[419, 415])).
% 2.49/2.66 tff(421,plain,(
% 2.49/2.66 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(skolemize,[status(sab)],[420])).
% 2.49/2.66 tff(422,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[421, 414])).
% 2.49/2.66 tff(423,plain,
% 2.49/2.66 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(424,plain,
% 2.49/2.66 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.49/2.66 inference(quant_inst,[status(thm)],[])).
% 2.49/2.66 tff(425,plain,
% 2.49/2.66 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[424, 423])).
% 2.49/2.66 tff(426,plain,
% 2.49/2.66 (m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.49/2.66 inference(unit_resolution,[status(thm)],[425, 422, 144])).
% 2.49/2.66 tff(427,plain,
% 2.49/2.66 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(428,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[427])).
% 2.49/2.66 tff(429,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(430,plain,
% 2.49/2.66 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(431,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[430])).
% 2.49/2.66 tff(432,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 2.49/2.66 tff(433,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[432, 431])).
% 2.49/2.66 tff(434,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[433, 429])).
% 2.49/2.66 tff(435,plain,(
% 2.49/2.66 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(skolemize,[status(sab)],[434])).
% 2.49/2.66 tff(436,plain,
% 2.49/2.66 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[435, 428])).
% 2.49/2.66 tff(437,plain,
% 2.49/2.66 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(438,plain,
% 2.49/2.66 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.66 inference(quant_inst,[status(thm)],[])).
% 2.49/2.66 tff(439,plain,
% 2.49/2.66 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(k1_tsp_2(A!0, B!1)) | (~m1_subset_1(k1_tsp_2(A!0, B!1), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[438, 437])).
% 2.49/2.66 tff(440,plain,
% 2.49/2.66 (v1_relat_1(k1_tsp_2(A!0, B!1))),
% 2.49/2.66 inference(unit_resolution,[status(thm)],[439, 436, 426])).
% 2.49/2.66 tff(441,plain,
% 2.49/2.66 (^[A: $i, B: $i] : refl((r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(442,plain,
% 2.49/2.66 (![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[441])).
% 2.49/2.66 tff(443,plain,
% 2.49/2.66 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(B) & v1_funct_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_funct_1(B))))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B))))), (((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> (((~v1_relat_1(B)) | (~v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)))), rewrite((((~v1_relat_1(B)) | (~v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))), (((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(444,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[443])).
% 2.49/2.66 tff(445,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(446,plain,
% 2.49/2.66 (^[A: $i, B: $i] : rewrite(((v1_relat_1(B) & v1_funct_1(B)) => r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(447,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A)) <=> ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[446])).
% 2.49/2.66 tff(448,axiom,(![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t145_funct_1')).
% 2.49/2.66 tff(449,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[448, 447])).
% 2.49/2.66 tff(450,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[449, 445])).
% 2.49/2.66 tff(451,plain,(
% 2.49/2.66 ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A))),
% 2.49/2.66 inference(skolemize,[status(sab)],[450])).
% 2.49/2.66 tff(452,plain,
% 2.49/2.66 (![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[451, 444])).
% 2.49/2.66 tff(453,plain,
% 2.49/2.66 (![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[452, 442])).
% 2.49/2.66 tff(454,plain,
% 2.49/2.66 (((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(455,plain,
% 2.49/2.66 ((r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1)))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(456,plain,
% 2.49/2.66 (((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 2.49/2.66 inference(monotonicity,[status(thm)],[455])).
% 2.49/2.66 tff(457,plain,
% 2.49/2.66 (((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.66 inference(transitivity,[status(thm)],[456, 454])).
% 2.49/2.66 tff(458,plain,
% 2.49/2.66 ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.66 inference(quant_inst,[status(thm)],[])).
% 2.49/2.66 tff(459,plain,
% 2.49/2.66 ((~![A: $i, B: $i] : (r1_tarski(k9_relat_1(B, k10_relat_1(B, A)), A) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2))) | (~v1_relat_1(k1_tsp_2(A!0, B!1)))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[458, 457])).
% 2.49/2.66 tff(460,plain,
% 2.49/2.66 (r1_tarski(k9_relat_1(k1_tsp_2(A!0, B!1), k10_relat_1(k1_tsp_2(A!0, B!1), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))), k1_struct_0(B!1, k8_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), k3_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(unit_resolution,[status(thm)],[459, 453, 148, 440])).
% 2.49/2.66 tff(461,plain,
% 2.49/2.66 (r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[460, 412])).
% 2.49/2.66 tff(462,plain,
% 2.49/2.66 ((~(r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) <=> ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))))) | (~r1_tarski(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)), k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))) | ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 2.49/2.66 inference(tautology,[status(thm)],[])).
% 2.49/2.66 tff(463,plain,
% 2.49/2.66 ((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(unit_resolution,[status(thm)],[462, 461, 247])).
% 2.49/2.66 tff(464,plain,
% 2.49/2.66 ((k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) <=> (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.66 inference(commutativity,[status(thm)],[])).
% 2.49/2.66 tff(465,plain,
% 2.49/2.66 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(466,plain,
% 2.49/2.66 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[465])).
% 2.49/2.66 tff(467,plain,
% 2.49/2.66 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(468,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[467])).
% 2.49/2.66 tff(469,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(470,plain,
% 2.49/2.66 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), trans(monotonicity(rewrite(((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) <=> (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B))), ((((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.66 inference(bind,[status(th)],[])).
% 2.49/2.66 tff(471,plain,
% 2.49/2.66 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.66 inference(quant_intro,[status(thm)],[470])).
% 2.49/2.66 tff(472,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k3_tsp_2(A, B), A, B)) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_tsp_2')).
% 2.49/2.66 tff(473,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[472, 471])).
% 2.49/2.66 tff(474,plain,
% 2.49/2.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[473, 469])).
% 2.49/2.66 tff(475,plain,(
% 2.49/2.66 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k3_tsp_2(A, B)) & v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A, B), A, B) & m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.66 inference(skolemize,[status(sab)],[474])).
% 2.49/2.66 tff(476,plain,
% 2.49/2.66 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[475, 468])).
% 2.49/2.66 tff(477,plain,
% 2.49/2.66 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.66 inference(modus_ponens,[status(thm)],[476, 466])).
% 2.49/2.66 tff(478,plain,
% 2.49/2.66 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.66 inference(rewrite,[status(thm)],[])).
% 2.49/2.66 tff(479,plain,
% 2.49/2.66 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(480,plain,
% 2.49/2.67 ((~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(481,plain,
% 2.49/2.67 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.67 inference(monotonicity,[status(thm)],[480])).
% 2.49/2.67 tff(482,plain,
% 2.49/2.67 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.67 inference(transitivity,[status(thm)],[481, 479])).
% 2.49/2.67 tff(483,plain,
% 2.49/2.67 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 2.49/2.67 inference(monotonicity,[status(thm)],[482])).
% 2.49/2.67 tff(484,plain,
% 2.49/2.67 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.67 inference(transitivity,[status(thm)],[483, 478])).
% 2.49/2.67 tff(485,plain,
% 2.49/2.67 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.49/2.67 inference(quant_inst,[status(thm)],[])).
% 2.49/2.67 tff(486,plain,
% 2.49/2.67 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k3_tsp_2(A, B))) | (~v1_funct_2(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k3_tsp_2(A, B), A, B)) | (~m2_relset_1(k3_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[485, 484])).
% 2.49/2.67 tff(487,plain,
% 2.49/2.67 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[486, 131, 130, 23, 88, 129, 477])).
% 2.49/2.67 tff(488,plain,
% 2.49/2.67 (~((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[487, 115])).
% 2.49/2.67 tff(489,plain,
% 2.49/2.67 (((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k3_tsp_2(A!0, B!1))),
% 2.49/2.67 inference(tautology,[status(thm)],[])).
% 2.49/2.67 tff(490,plain,
% 2.49/2.67 (v1_funct_1(k3_tsp_2(A!0, B!1))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[489, 488])).
% 2.49/2.67 tff(491,plain,
% 2.49/2.67 (((~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k3_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.49/2.67 inference(tautology,[status(thm)],[])).
% 2.49/2.67 tff(492,plain,
% 2.49/2.67 (v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[491, 488])).
% 2.49/2.67 tff(493,plain,
% 2.49/2.67 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.49/2.67 inference(monotonicity,[status(thm)],[235])).
% 2.49/2.67 tff(494,plain,
% 2.49/2.67 (m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[262, 493])).
% 2.49/2.67 tff(495,plain,
% 2.49/2.67 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(496,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[495])).
% 2.49/2.67 tff(497,plain,
% 2.49/2.67 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> (((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))))), rewrite((((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(498,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[497])).
% 2.49/2.67 tff(499,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(500,plain,
% 2.49/2.67 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(501,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[500])).
% 2.49/2.67 tff(502,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_pre_topc')).
% 2.49/2.67 tff(503,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[502, 501])).
% 2.49/2.67 tff(504,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[503, 499])).
% 2.49/2.67 tff(505,plain,(
% 2.49/2.67 ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)))),
% 2.49/2.67 inference(skolemize,[status(sab)],[504])).
% 2.49/2.67 tff(506,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[505, 498])).
% 2.49/2.67 tff(507,plain,
% 2.49/2.67 (![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[506, 496])).
% 2.49/2.67 tff(508,plain,
% 2.49/2.67 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(509,plain,
% 2.49/2.67 (((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(510,plain,
% 2.49/2.67 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))))),
% 2.49/2.67 inference(monotonicity,[status(thm)],[509])).
% 2.49/2.67 tff(511,plain,
% 2.49/2.67 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))))),
% 2.49/2.67 inference(transitivity,[status(thm)],[510, 508])).
% 2.49/2.67 tff(512,plain,
% 2.49/2.67 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.49/2.67 inference(quant_inst,[status(thm)],[])).
% 2.49/2.67 tff(513,plain,
% 2.49/2.67 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[512, 511])).
% 2.49/2.67 tff(514,plain,
% 2.49/2.67 ((~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[513, 507, 27])).
% 2.49/2.67 tff(515,plain,
% 2.49/2.67 (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[514, 494, 492, 490, 67])).
% 2.49/2.67 tff(516,plain,
% 2.49/2.67 (r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))) <=> r2_hidden(C!2, u1_struct_0(A!0))),
% 2.49/2.67 inference(monotonicity,[status(thm)],[155])).
% 2.49/2.67 tff(517,plain,
% 2.49/2.67 (r2_hidden(C!2, u1_struct_0(A!0)) <=> r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 2.49/2.67 inference(symmetry,[status(thm)],[516])).
% 2.49/2.67 tff(518,plain,
% 2.49/2.67 (^[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))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(519,plain,
% 2.49/2.67 (![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)))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[518])).
% 2.49/2.67 tff(520,plain,
% 2.49/2.67 (![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)))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(521,plain,
% 2.49/2.67 (^[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))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(522,plain,
% 2.49/2.67 (![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)))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[521])).
% 2.49/2.67 tff(523,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')).
% 2.49/2.67 tff(524,plain,
% 2.49/2.67 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[523, 522])).
% 2.49/2.67 tff(525,plain,
% 2.49/2.67 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[524, 520])).
% 2.49/2.67 tff(526,plain,(
% 2.49/2.67 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.49/2.67 inference(skolemize,[status(sab)],[525])).
% 2.49/2.67 tff(527,plain,
% 2.49/2.67 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[526, 519])).
% 2.49/2.67 tff(528,plain,
% 2.49/2.67 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(529,plain,
% 2.49/2.67 ((r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(530,plain,
% 2.49/2.67 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0))))),
% 2.49/2.67 inference(monotonicity,[status(thm)],[529])).
% 2.49/2.67 tff(531,plain,
% 2.49/2.67 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0)))),
% 2.49/2.67 inference(transitivity,[status(thm)],[530, 528])).
% 2.49/2.67 tff(532,plain,
% 2.49/2.67 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 2.49/2.67 inference(quant_inst,[status(thm)],[])).
% 2.49/2.67 tff(533,plain,
% 2.49/2.67 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[532, 531])).
% 2.49/2.67 tff(534,plain,
% 2.49/2.67 (v1_xboole_0(u1_struct_0(A!0)) | r2_hidden(C!2, u1_struct_0(A!0))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[533, 181, 527])).
% 2.49/2.67 tff(535,plain,
% 2.49/2.67 (r2_hidden(C!2, u1_struct_0(A!0))),
% 2.49/2.67 inference(unit_resolution,[status(thm)],[534, 283])).
% 2.49/2.67 tff(536,plain,
% 2.49/2.67 (r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[535, 517])).
% 2.49/2.67 tff(537,plain,
% 2.49/2.67 (^[A: $i, B: $i] : refl(((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(538,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[537])).
% 2.49/2.67 tff(539,plain,
% 2.49/2.67 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(B) & v1_funct_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_funct_1(B))))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B))))), (((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | ((~v1_relat_1(B)) | (~v1_funct_1(B)))))), rewrite(((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | ((~v1_relat_1(B)) | (~v1_funct_1(B)))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))), (((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(540,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[539])).
% 2.49/2.67 tff(541,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(542,plain,
% 2.49/2.67 (^[A: $i, B: $i] : trans(monotonicity(rewrite((r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A)))) <=> ((~r2_hidden(A, k1_relat_1(B))) | (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))), (((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ((v1_relat_1(B) & v1_funct_1(B)) => ((~r2_hidden(A, k1_relat_1(B))) | (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))))), rewrite(((v1_relat_1(B) & v1_funct_1(B)) => ((~r2_hidden(A, k1_relat_1(B))) | (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))), (((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))))),
% 2.49/2.67 inference(bind,[status(th)],[])).
% 2.49/2.67 tff(543,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))))) <=> ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 2.49/2.67 inference(quant_intro,[status(thm)],[542])).
% 2.49/2.67 tff(544,axiom,(![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (r2_hidden(A, k1_relat_1(B)) => (k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t117_funct_1')).
% 2.49/2.67 tff(545,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[544, 543])).
% 2.49/2.67 tff(546,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[545, 541])).
% 2.49/2.67 tff(547,plain,(
% 2.49/2.67 ![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~(v1_relat_1(B) & v1_funct_1(B))))),
% 2.49/2.67 inference(skolemize,[status(sab)],[546])).
% 2.49/2.67 tff(548,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[547, 540])).
% 2.49/2.67 tff(549,plain,
% 2.49/2.67 (![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 2.49/2.67 inference(modus_ponens,[status(thm)],[548, 538])).
% 2.49/2.67 tff(550,plain,
% 2.49/2.67 (((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 2.49/2.67 inference(rewrite,[status(thm)],[])).
% 2.49/2.67 tff(551,plain,
% 2.49/2.67 (((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1)))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(552,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))))))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[551])).
% 2.49/2.68 tff(553,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))))),
% 2.49/2.68 inference(transitivity,[status(thm)],[552, 550])).
% 2.49/2.68 tff(554,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.68 inference(quant_inst,[status(thm)],[])).
% 2.49/2.68 tff(555,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : ((k9_relat_1(B, k1_tarski(A)) = k1_tarski(k1_funct_1(B, A))) | (~r2_hidden(A, k1_relat_1(B))) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[554, 553])).
% 2.49/2.68 tff(556,plain,
% 2.49/2.68 ((k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))) | (~r2_hidden(C!2, k1_relat_1(k1_tsp_2(A!0, B!1))))),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[555, 549, 148, 440])).
% 2.49/2.68 tff(557,plain,
% 2.49/2.68 (k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[556, 536])).
% 2.49/2.68 tff(558,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(559,plain,
% 2.49/2.68 ((v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(560,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2))))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[559])).
% 2.49/2.68 tff(561,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)))),
% 2.49/2.68 inference(transitivity,[status(thm)],[560, 558])).
% 2.49/2.68 tff(562,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2)) | (~l1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 2.49/2.68 inference(quant_inst,[status(thm)],[])).
% 2.49/2.68 tff(563,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k1_struct_0(A, B) = k1_tarski(B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (k1_struct_0(A!0, C!2) = k1_tarski(C!2))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[562, 561])).
% 2.49/2.68 tff(564,plain,
% 2.49/2.68 (k1_struct_0(A!0, C!2) = k1_tarski(C!2)),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[563, 131, 181, 317, 27])).
% 2.49/2.68 tff(565,plain,
% 2.49/2.68 (k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k1_tsp_2(A!0, B!1), k1_tarski(C!2))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[234, 564])).
% 2.49/2.68 tff(566,plain,
% 2.49/2.68 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(567,plain,
% 2.49/2.68 (((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(568,plain,
% 2.49/2.68 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)))))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[567])).
% 2.49/2.68 tff(569,plain,
% 2.49/2.68 (((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))))),
% 2.49/2.68 inference(transitivity,[status(thm)],[568, 566])).
% 2.49/2.68 tff(570,plain,
% 2.49/2.68 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.49/2.68 inference(quant_inst,[status(thm)],[])).
% 2.49/2.68 tff(571,plain,
% 2.49/2.68 ((~![A: $i, B: $i, C: $i, D: $i] : ((k4_pre_topc(A, B, C, D) = k9_relat_1(C, D)) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[570, 569])).
% 2.49/2.68 tff(572,plain,
% 2.49/2.68 ((~l1_struct_0(B!1)) | (~v1_funct_1(k3_tsp_2(A!0, B!1))) | (~v1_funct_2(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k3_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)))),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[571, 507, 27])).
% 2.49/2.68 tff(573,plain,
% 2.49/2.68 (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2))),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[572, 494, 492, 490, 67])).
% 2.49/2.68 tff(574,plain,
% 2.49/2.68 (k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))),
% 2.49/2.68 inference(transitivity,[status(thm)],[573, 565, 557])).
% 2.49/2.68 tff(575,plain,
% 2.49/2.68 ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) <=> (k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)) = k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[574, 515])).
% 2.49/2.68 tff(576,plain,
% 2.49/2.68 ((k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2))) <=> (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.68 inference(transitivity,[status(thm)],[575, 464])).
% 2.49/2.68 tff(577,plain,
% 2.49/2.68 ((~(k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))) <=> (~(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[576])).
% 2.49/2.68 tff(578,plain,
% 2.49/2.68 (~(k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k1_struct_0(A!0, C!2)) = k4_pre_topc(A!0, B!1, k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)))),
% 2.49/2.68 inference(or_elim,[status(thm)],[180])).
% 2.49/2.68 tff(579,plain,
% 2.49/2.68 (~(k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[578, 577])).
% 2.49/2.68 tff(580,plain,
% 2.49/2.68 ((~((k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2))))) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0) | (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_tarski(k1_funct_1(k1_tsp_2(A!0, B!1), C!2)))),
% 2.49/2.68 inference(tautology,[status(thm)],[])).
% 2.49/2.68 tff(581,plain,
% 2.49/2.68 (k9_relat_1(k3_tsp_2(A!0, B!1), k4_tex_4(A!0, C!2)) = k1_xboole_0),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[580, 579, 463])).
% 2.49/2.68 tff(582,plain,
% 2.49/2.68 (k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[581, 238])).
% 2.49/2.68 tff(583,plain,
% 2.49/2.68 (^[A: $i, B: $i] : refl(((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))) <=> ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))),
% 2.49/2.68 inference(bind,[status(th)],[])).
% 2.49/2.68 tff(584,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))) <=> ![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 2.49/2.68 inference(quant_intro,[status(thm)],[583])).
% 2.49/2.68 tff(585,plain,
% 2.49/2.68 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)) <=> (~((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))), ((~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))) <=> (~(~((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))))), rewrite((~(~((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))) <=> ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))), ((~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))) <=> ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0))))), (((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((~v1_relat_1(B)) | ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))))), rewrite(((~v1_relat_1(B)) | ((A = k1_xboole_0) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) <=> ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))), (((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))))),
% 2.49/2.68 inference(bind,[status(th)],[])).
% 2.49/2.68 tff(586,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 2.49/2.68 inference(quant_intro,[status(thm)],[585])).
% 2.49/2.68 tff(587,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(588,plain,
% 2.49/2.68 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0))) <=> (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))), ((v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> (v1_relat_1(B) => (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))))), rewrite((v1_relat_1(B) => (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))), ((v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))))),
% 2.49/2.68 inference(bind,[status(th)],[])).
% 2.49/2.68 tff(589,plain,
% 2.49/2.68 (![A: $i, B: $i] : (v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 2.49/2.68 inference(quant_intro,[status(thm)],[588])).
% 2.49/2.68 tff(590,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => (~(((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B))) & (k9_relat_1(B, A) = k1_xboole_0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t152_relat_1')).
% 2.49/2.68 tff(591,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[590, 589])).
% 2.49/2.68 tff(592,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[591, 587])).
% 2.49/2.68 tff(593,plain,(
% 2.49/2.68 ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~(A = k1_xboole_0)) & r1_tarski(A, k1_relat_1(B)) & (k9_relat_1(B, A) = k1_xboole_0))))),
% 2.49/2.68 inference(skolemize,[status(sab)],[592])).
% 2.49/2.68 tff(594,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[593, 586])).
% 2.49/2.68 tff(595,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[594, 584])).
% 2.49/2.68 tff(596,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))) <=> ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(597,plain,
% 2.49/2.68 (((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))) <=> ((~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(598,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))) <=> ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))))),
% 2.49/2.68 inference(monotonicity,[status(thm)],[597])).
% 2.49/2.68 tff(599,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))) <=> ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 2.49/2.68 inference(transitivity,[status(thm)],[598, 596])).
% 2.49/2.68 tff(600,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0)))),
% 2.49/2.68 inference(quant_inst,[status(thm)],[])).
% 2.49/2.68 tff(601,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : ((A = k1_xboole_0) | (~v1_relat_1(B)) | (~r1_tarski(A, k1_relat_1(B))) | (~(k9_relat_1(B, A) = k1_xboole_0)))) | (~v1_relat_1(k1_tsp_2(A!0, B!1))) | (k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[600, 599])).
% 2.49/2.68 tff(602,plain,
% 2.49/2.68 ((k2_tex_4(A!0, C!2) = k1_xboole_0) | (~r1_tarski(k2_tex_4(A!0, C!2), k1_relat_1(k1_tsp_2(A!0, B!1)))) | (~(k9_relat_1(k1_tsp_2(A!0, B!1), k2_tex_4(A!0, C!2)) = k1_xboole_0))),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[601, 595, 440])).
% 2.49/2.68 tff(603,plain,
% 2.49/2.68 (k2_tex_4(A!0, C!2) = k1_xboole_0),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[602, 582, 192])).
% 2.49/2.68 tff(604,plain,
% 2.49/2.68 (k4_tex_4(A!0, C!2) = k1_xboole_0),
% 2.49/2.68 inference(transitivity,[status(thm)],[212, 603])).
% 2.49/2.68 tff(605,plain,
% 2.49/2.68 (v1_xboole_0(k4_tex_4(A!0, C!2)) <=> v1_xboole_0(k1_xboole_0)),
% 2.49/2.68 inference(monotonicity,[status(thm)],[604])).
% 2.49/2.68 tff(606,plain,
% 2.49/2.68 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k4_tex_4(A!0, C!2))),
% 2.49/2.68 inference(symmetry,[status(thm)],[605])).
% 2.49/2.68 tff(607,plain,
% 2.49/2.68 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(608,axiom,(((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)) & v5_membered(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_membered')).
% 2.49/2.68 tff(609,plain,
% 2.49/2.68 ((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)),
% 2.49/2.68 inference(and_elim,[status(thm)],[608])).
% 2.49/2.68 tff(610,plain,
% 2.49/2.68 (((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)),
% 2.49/2.68 inference(and_elim,[status(thm)],[609])).
% 2.49/2.68 tff(611,plain,
% 2.49/2.68 ((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)),
% 2.49/2.68 inference(and_elim,[status(thm)],[610])).
% 2.49/2.68 tff(612,plain,
% 2.49/2.68 (v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)),
% 2.49/2.68 inference(and_elim,[status(thm)],[611])).
% 2.49/2.68 tff(613,plain,
% 2.49/2.68 (v1_xboole_0(k1_xboole_0)),
% 2.49/2.68 inference(and_elim,[status(thm)],[612])).
% 2.49/2.68 tff(614,plain,
% 2.49/2.68 (v1_xboole_0(k1_xboole_0)),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[613, 607])).
% 2.49/2.68 tff(615,plain,
% 2.49/2.68 (v1_xboole_0(k4_tex_4(A!0, C!2))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[614, 606])).
% 2.49/2.68 tff(616,plain,
% 2.49/2.68 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))))),
% 2.49/2.68 inference(bind,[status(th)],[])).
% 2.49/2.68 tff(617,plain,
% 2.49/2.68 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 2.49/2.68 inference(quant_intro,[status(thm)],[616])).
% 2.49/2.68 tff(618,plain,
% 2.49/2.68 (^[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))) | (~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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_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) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite(((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 2.49/2.68 inference(bind,[status(th)],[])).
% 2.49/2.68 tff(619,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 2.49/2.68 inference(quant_intro,[status(thm)],[618])).
% 2.49/2.68 tff(620,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(621,plain,
% 2.49/2.68 (^[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))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(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))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 2.49/2.68 inference(bind,[status(th)],[])).
% 2.49/2.68 tff(622,plain,
% 2.49/2.68 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & m1_subset_1(B, u1_struct_0(A))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 2.49/2.68 inference(quant_intro,[status(thm)],[621])).
% 2.49/2.68 tff(623,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))) => ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_tex_4')).
% 2.49/2.68 tff(624,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[623, 622])).
% 2.49/2.68 tff(625,plain,
% 2.49/2.68 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[624, 620])).
% 2.49/2.68 tff(626,plain,(
% 2.49/2.68 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))) | ((~v1_xboole_0(k4_tex_4(A, B))) & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 2.49/2.68 inference(skolemize,[status(sab)],[625])).
% 2.49/2.68 tff(627,plain,
% 2.49/2.68 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[626, 619])).
% 2.49/2.68 tff(628,plain,
% 2.49/2.68 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[627, 617])).
% 2.49/2.68 tff(629,plain,
% 2.49/2.68 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 2.49/2.68 inference(rewrite,[status(thm)],[])).
% 2.49/2.68 tff(630,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 2.49/2.68 inference(quant_inst,[status(thm)],[])).
% 2.49/2.68 tff(631,plain,
% 2.49/2.68 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~(v1_xboole_0(k4_tex_4(A, B)) | (~m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 2.49/2.68 inference(modus_ponens,[status(thm)],[630, 629])).
% 2.49/2.68 tff(632,plain,
% 2.49/2.68 (~(v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 2.49/2.68 inference(unit_resolution,[status(thm)],[631, 131, 130, 23, 181, 628])).
% 2.49/2.69 tff(633,plain,
% 2.49/2.69 ((v1_xboole_0(k4_tex_4(A!0, C!2)) | (~m1_subset_1(k4_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) | (~v1_xboole_0(k4_tex_4(A!0, C!2)))),
% 2.49/2.69 inference(tautology,[status(thm)],[])).
% 2.49/2.69 tff(634,plain,
% 2.49/2.69 (~v1_xboole_0(k4_tex_4(A!0, C!2))),
% 2.49/2.69 inference(unit_resolution,[status(thm)],[633, 632])).
% 2.49/2.69 tff(635,plain,
% 2.49/2.69 ($false),
% 2.49/2.69 inference(unit_resolution,[status(thm)],[634, 615])).
% 2.49/2.69 % SZS output end Proof
% 2.49/2.71 % E exiting
%------------------------------------------------------------------------------