%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP025+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:42:38 AM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP025+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:51:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(v4_pre_topc_type, type, (
% 0.21/0.42 v4_pre_topc: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_A_0_type, type, (
% 0.21/0.42 tptp_fun_A_0: $i)).
% 0.21/0.42 tff(tptp_fun_B_1_type, type, (
% 0.21/0.42 tptp_fun_B_1: $i)).
% 0.21/0.42 tff(k3_tex_4_type, type, (
% 0.21/0.42 k3_tex_4: ( $i * $i ) > $i)).
% 0.21/0.42 tff(u1_struct_0_type, type, (
% 0.21/0.42 u1_struct_0: $i > $i)).
% 0.21/0.42 tff(v1_tsp_1_type, type, (
% 0.21/0.42 v1_tsp_1: ( $i * $i ) > $o)).
% 0.21/0.42 tff(v1_tsp_2_type, type, (
% 0.21/0.42 v1_tsp_2: ( $i * $i ) > $o)).
% 0.21/0.42 tff(m1_subset_1_type, type, (
% 0.21/0.42 m1_subset_1: ( $i * $i ) > $o)).
% 0.21/0.42 tff(k1_zfmisc_1_type, type, (
% 0.21/0.42 k1_zfmisc_1: $i > $i)).
% 0.21/0.42 tff(v2_pre_topc_type, type, (
% 0.21/0.42 v2_pre_topc: $i > $o)).
% 0.21/0.42 tff(l1_pre_topc_type, type, (
% 0.21/0.42 l1_pre_topc: $i > $o)).
% 0.21/0.42 tff(v3_struct_0_type, type, (
% 0.21/0.42 v3_struct_0: $i > $o)).
% 0.21/0.42 tff(v1_tex_2_type, type, (
% 0.21/0.42 v1_tex_2: ( $i * $i ) > $o)).
% 0.21/0.42 tff(v3_pre_topc_type, type, (
% 0.21/0.42 v3_pre_topc: ( $i * $i ) > $o)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 ((u1_struct_0(A!0) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.21/0.42 inference(commutativity,[status(thm)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[5, 3])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (^[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] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.42 tff(12,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_tsp_2')).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.42 tff(15,plain,(
% 0.21/0.42 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[14])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (~((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)) & v1_tsp_2(B!1, A!0) & v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)) & v1_tsp_2(B!1, A!0) & v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A)) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(21,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (~(((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A)) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_tsp_2')).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((v3_pre_topc(B, A) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)) & v1_tsp_2(B!1, A!0) & v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (l1_pre_topc(A!0)),
% 0.21/0.43 inference(and_elim,[status(thm)],[26])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (v2_pre_topc(A!0)),
% 0.21/0.43 inference(and_elim,[status(thm)],[26])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (~v3_struct_0(A!0)),
% 0.21/0.43 inference(and_elim,[status(thm)],[26])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~(((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))) <=> v1_tsp_2(B, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[32, 29, 28, 27, 17])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (~((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)) & v1_tsp_2(B!1, A!0) & v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.21/0.43 inference(and_elim,[status(thm)],[26])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.21/0.43 inference(or_elim,[status(thm)],[34])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))) <=> v1_tsp_2(B, A!0))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (~(((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[38, 35, 33])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 ((v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)) & v1_tsp_2(B!1, A!0) & v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.21/0.43 inference(or_elim,[status(thm)],[34])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (v1_tsp_2(B!1, A!0)),
% 0.21/0.43 inference(and_elim,[status(thm)],[40])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 ((((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0)) | (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))) | (~v1_tsp_2(B!1, A!0))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 ((((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) <=> v1_tsp_2(B!1, A!0)) | (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[43, 39])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = u1_struct_0(A!0))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (k3_tex_4(A!0, B!1) = u1_struct_0(A!0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 ((k3_tex_4(A!0, B!1) = B!1) <=> (u1_struct_0(A!0) = B!1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 ((k3_tex_4(A!0, B!1) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.21/0.43 inference(transitivity,[status(thm)],[47, 1])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 ((B!1 = u1_struct_0(A!0)) <=> (k3_tex_4(A!0, B!1) = B!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[48])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 ((~(B!1 = u1_struct_0(A!0))) <=> (~(k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[49])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl(((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(rewrite((v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))) <=> (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))), rewrite((~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))) <=> (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))), ((v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))) <=> (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A)))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A)))) <=> ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.43 tff(56,axiom,(![A: $i, B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_tex_2')).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.21/0.43 tff(59,plain,(
% 0.21/0.43 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[58])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~((B = A) <=> v1_tex_2(B, k1_zfmisc_1(A)))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (~((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[63, 35, 60])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[40])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(B!1 = u1_struct_0(A!0))) | (~v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (((B!1 = u1_struct_0(A!0)) <=> v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~(B!1 = u1_struct_0(A!0)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (~(B!1 = u1_struct_0(A!0))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (~(k3_tex_4(A!0, B!1) = B!1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[68, 50])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((v4_pre_topc(B, A) => (k3_tex_4(A, B) = B)) <=> ((~v4_pre_topc(B, A)) | (k3_tex_4(A, B) = B))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v4_pre_topc(B, A)) | (k3_tex_4(A, B) = B))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v4_pre_topc(B, A)) | (k3_tex_4(A, B) = B))) <=> ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.44 tff(82,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(B, A) => (k3_tex_4(A, B) = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t62_tex_4')).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.44 tff(85,plain,(
% 0.21/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[84])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[87, 71])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B, A!0)))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B, A!0))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[94, 29, 28, 27, 88])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v4_pre_topc(B!1, A!0))) <=> ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v4_pre_topc(B!1, A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v4_pre_topc(B!1, A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.44 inference(transitivity,[status(thm)],[98, 96])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v4_pre_topc(B!1, A!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v4_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 ((~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[101, 35, 95])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (~v4_pre_topc(B!1, A!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[102, 69])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (^[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_pre_topc(B, A) => (k3_tex_4(A, B) = B)) <=> ((~v3_pre_topc(B, A)) | (k3_tex_4(A, B) = B))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_pre_topc(B, A)) | (k3_tex_4(A, B) = B))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v3_pre_topc(B, A)) | (k3_tex_4(A, B) = B))) <=> ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))) <=> ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.44 tff(116,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v3_pre_topc(B, A) => (k3_tex_4(A, B) = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t58_tex_4')).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.21/0.44 tff(119,plain,(
% 0.21/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[118])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))) | (~v2_pre_topc(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 105])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0)))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[125, 123])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((k3_tex_4(A!0, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B, A!0))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((k3_tex_4(A, B) = B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v3_pre_topc(B, A))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[128, 29, 28, 27, 122])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v3_pre_topc(B!1, A!0))) <=> ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v3_pre_topc(B!1, A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[131])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v3_pre_topc(B!1, A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1))),
% 0.21/0.45 inference(transitivity,[status(thm)],[132, 130])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B!1) = B!1) | (~v3_pre_topc(B!1, A!0)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 ((~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[135, 35, 129])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (~v3_pre_topc(B!1, A!0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[136, 69])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 (v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)),
% 0.21/0.45 inference(and_elim,[status(thm)],[40])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[138, 137, 103])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------