TSTP Solution File: TOP025+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP025+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 30 01:55:52 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP025+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 09:32:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(v4_pre_topc_type, type, (
% 0.20/0.43 v4_pre_topc: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_A_0_type, type, (
% 0.20/0.43 tptp_fun_A_0: $i)).
% 0.20/0.43 tff(tptp_fun_B_1_type, type, (
% 0.20/0.43 tptp_fun_B_1: $i)).
% 0.20/0.43 tff(k3_tex_4_type, type, (
% 0.20/0.43 k3_tex_4: ( $i * $i ) > $i)).
% 0.20/0.43 tff(u1_struct_0_type, type, (
% 0.20/0.43 u1_struct_0: $i > $i)).
% 0.20/0.43 tff(v1_tsp_1_type, type, (
% 0.20/0.43 v1_tsp_1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(v1_tsp_2_type, type, (
% 0.20/0.43 v1_tsp_2: ( $i * $i ) > $o)).
% 0.20/0.43 tff(m1_subset_1_type, type, (
% 0.20/0.43 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(k1_zfmisc_1_type, type, (
% 0.20/0.43 k1_zfmisc_1: $i > $i)).
% 0.20/0.43 tff(v2_pre_topc_type, type, (
% 0.20/0.43 v2_pre_topc: $i > $o)).
% 0.20/0.43 tff(l1_pre_topc_type, type, (
% 0.20/0.43 l1_pre_topc: $i > $o)).
% 0.20/0.43 tff(v3_struct_0_type, type, (
% 0.20/0.43 v3_struct_0: $i > $o)).
% 0.20/0.43 tff(v1_tex_2_type, type, (
% 0.20/0.43 v1_tex_2: ( $i * $i ) > $o)).
% 0.20/0.43 tff(v3_pre_topc_type, type, (
% 0.20/0.43 v3_pre_topc: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 ((u1_struct_0(A!0) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (^[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_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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![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_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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (^[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_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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![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_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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (![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_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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (^[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))))), 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) | (~l1_pre_topc(A)) | (~v2_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) | (~l1_pre_topc(A)) | (~v2_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_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) | (~l1_pre_topc(A)) | (~v2_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))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![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)))) | (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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![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)))) | (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))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (^[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] : 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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (![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))) => (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))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.44 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/sandbox2/benchmark/theBenchmark.p','d5_tsp_2')).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (![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)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (![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)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.44 tff(15,plain,(
% 0.20/0.44 ![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)))) | (v1_tsp_2(B, A) <=> (v1_tsp_1(B, A) & (k3_tex_4(A, B) = u1_struct_0(A))))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[14])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 ((((~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))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 ((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (((~(~((~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))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (((~(~((~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))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 ((~![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) | 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))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 ((~![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) | 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))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(24,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/sandbox2/benchmark/theBenchmark.p','t3_tsp_2')).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (~![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) | v4_pre_topc(B, A)) & v1_tsp_2(B, A) & v1_tex_2(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 ((~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)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (l1_pre_topc(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (v2_pre_topc(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (~v3_struct_0(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (((~![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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (v1_tsp_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 ((~![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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 ((~![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_2(B, A) <=> (~((~v1_tsp_1(B, A)) | (~(k3_tex_4(A, B) = u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 17])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (~((~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))))))),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.44 inference(or_elim,[status(thm)],[40])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | ((~m1_subset_1(B!1, k1_zfmisc_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)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | (~m1_subset_1(B!1, k1_zfmisc_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)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | ((~m1_subset_1(B!1, k1_zfmisc_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)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (v1_tsp_2(B, A!0) <=> (~((~v1_tsp_1(B, A!0)) | (~(k3_tex_4(A!0, B) = u1_struct_0(A!0)))))))) | (~m1_subset_1(B!1, k1_zfmisc_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))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (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)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[44, 41, 39])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 ((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)))),
% 0.20/0.44 inference(or_elim,[status(thm)],[40])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (v1_tsp_2(B!1, A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[46])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~(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)) | (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 ((~(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_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (~((~v1_tsp_1(B!1, A!0)) | (~(k3_tex_4(A!0, B!1) = u1_struct_0(A!0))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[49, 45])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (((~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))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (k3_tex_4(A!0, B!1) = u1_struct_0(A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 ((k3_tex_4(A!0, B!1) = B!1) <=> (u1_struct_0(A!0) = B!1)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 ((k3_tex_4(A!0, B!1) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.20/0.44 inference(transitivity,[status(thm)],[53, 1])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ((B!1 = u1_struct_0(A!0)) <=> (k3_tex_4(A!0, B!1) = B!1)),
% 0.20/0.44 inference(symmetry,[status(thm)],[54])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 ((~(B!1 = u1_struct_0(A!0))) <=> (~(k3_tex_4(A!0, B!1) = B!1))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (^[A: $i, B: $i] : refl(((~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))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![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))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![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))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (^[A: $i, B: $i] : rewrite((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))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![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))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.44 tff(62,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/sandbox2/benchmark/theBenchmark.p','t5_tex_2')).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.45 tff(65,plain,(
% 0.20/0.45 ![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[64])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))) | ((~m1_subset_1(B!1, k1_zfmisc_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)))))) <=> ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))) | (~m1_subset_1(B!1, k1_zfmisc_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)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))) | ((~m1_subset_1(B!1, k1_zfmisc_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)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | (v1_tex_2(B, k1_zfmisc_1(A)) <=> (~(B = A))))) | (~m1_subset_1(B!1, k1_zfmisc_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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))) <=> (~(B!1 = u1_struct_0(A!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[69, 41, 66])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.45 inference(and_elim,[status(thm)],[46])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 ((~(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)))) | (~(B!1 = u1_struct_0(A!0)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 ((~(v1_tex_2(B!1, k1_zfmisc_1(u1_struct_0(A!0))) <=> (~(B!1 = u1_struct_0(A!0))))) | (~(B!1 = u1_struct_0(A!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (~(B!1 = u1_struct_0(A!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (~(k3_tex_4(A!0, B!1) = B!1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[74, 56])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (^[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))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.45 tff(88,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/sandbox2/benchmark/theBenchmark.p','t62_tex_4')).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.45 tff(91,plain,(
% 0.20/0.45 ![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))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[90])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (![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)))) | (~v4_pre_topc(B, A))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[93, 77])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (((~![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)))) | (~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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 ((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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (((~![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)))) | (~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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (((~![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)))) | (~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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 ((~![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)))) | (~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))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 ((~![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)))) | (~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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[100, 35, 34, 33, 94])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (((~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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (((~![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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 ((~![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)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 ((~v4_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[107, 41, 101])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (~v4_pre_topc(B!1, A!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[108, 75])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (^[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))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.46 tff(122,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/sandbox2/benchmark/theBenchmark.p','t58_tex_4')).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.46 tff(125,plain,(
% 0.20/0.46 ![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))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[124])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[127, 111])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (((~![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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 ((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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (((~![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)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (((~![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))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 ((~![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))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[134, 35, 34, 33, 128])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (((~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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, B) = B) | (~v3_pre_topc(B, A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 ((~v3_pre_topc(B!1, A!0)) | (k3_tex_4(A!0, B!1) = B!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[141, 41, 135])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (~v3_pre_topc(B!1, A!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[142, 75])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (v3_pre_topc(B!1, A!0) | v4_pre_topc(B!1, A!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[46])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[144, 143, 109])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------