TSTP Solution File: TOP026+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP026+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 01:55:53 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : TOP026+1 : TPTP v8.1.0. Released v3.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 : Mon Aug 29 09:39:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(k3_tex_4_type, type, (
% 0.20/0.46 k3_tex_4: ( $i * $i ) > $i)).
% 0.20/0.46 tff(k5_subset_1_type, type, (
% 0.20/0.46 k5_subset_1: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_B_1_type, type, (
% 0.20/0.46 tptp_fun_B_1: $i)).
% 0.20/0.46 tff(u1_struct_0_type, type, (
% 0.20/0.46 u1_struct_0: $i > $i)).
% 0.20/0.46 tff(tptp_fun_A_0_type, type, (
% 0.20/0.46 tptp_fun_A_0: $i)).
% 0.20/0.46 tff(v4_pre_topc_type, type, (
% 0.20/0.46 v4_pre_topc: ( $i * $i ) > $o)).
% 0.20/0.46 tff(m1_subset_1_type, type, (
% 0.20/0.46 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.46 tff(k1_zfmisc_1_type, type, (
% 0.20/0.46 k1_zfmisc_1: $i > $i)).
% 0.20/0.46 tff(v1_tsp_2_type, type, (
% 0.20/0.46 v1_tsp_2: ( $i * $i ) > $o)).
% 0.20/0.46 tff(v2_pre_topc_type, type, (
% 0.20/0.46 v2_pre_topc: $i > $o)).
% 0.20/0.46 tff(l1_pre_topc_type, type, (
% 0.20/0.46 l1_pre_topc: $i > $o)).
% 0.20/0.46 tff(v3_struct_0_type, type, (
% 0.20/0.46 v3_struct_0: $i > $o)).
% 0.20/0.46 tff(k6_pre_topc_type, type, (
% 0.20/0.46 k6_pre_topc: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_C_2_type, type, (
% 0.20/0.46 tptp_fun_C_2: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (^[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] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(11,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(trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))) <=> ((~v4_pre_topc(C, A)) | (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~v4_pre_topc(C, A)) | (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ((~v4_pre_topc(C, A)) | (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))) <=> ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))), ((v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))) <=> (v1_tsp_2(B, A) => ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))), rewrite((v1_tsp_2(B, A) => ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) <=> ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))), ((v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))) <=> ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ((~v1_tsp_2(B, A)) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))) <=> ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))) <=> ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, 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) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, 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) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(12,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))) => (v1_tsp_2(B, A) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.46 tff(13,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) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (v4_pre_topc(C, A) => (C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_tsp_2')).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.46 tff(16,plain,(
% 0.20/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[15])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))) | (~v2_pre_topc(A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (((~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & (~(~v1_tsp_2(B!1, A!0))) & (~(~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ((~(~((~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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & ((~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & (~(~v1_tsp_2(B!1, A!0))) & (~(~m1_subset_1(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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[22, 21])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (((~(~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)))) & ((~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & (~(~v1_tsp_2(B!1, A!0))) & (~(~m1_subset_1(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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[23, 20])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 ((~![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) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,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) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_tsp_2')).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k6_pre_topc(A, C) = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, k6_pre_topc(A, C))))) | (~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) & v1_tsp_2(B!1, A!0) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (l1_pre_topc(A!0)),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (v2_pre_topc(A!0)),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (~v3_struct_0(A!0)),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : ((~v1_tsp_2(B, A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((C = k3_tex_4(A, k5_subset_1(u1_struct_0(A), B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v4_pre_topc(C, A)))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[44, 38, 37, 36, 19])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (v1_tsp_2(B!1, A!0)),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))) <=> ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v4_pre_topc(C, A!0)))) <=> ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v4_pre_topc(C, A!0))))) <=> ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v4_pre_topc(C, A!0))))) <=> ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | ((~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))) | (~v4_pre_topc(C, A!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 ((~![B: $i] : ((~v1_tsp_2(B, A!0)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B, C))) | (~v4_pre_topc(C, A!0))))) | (~v1_tsp_2(B!1, A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[53, 47, 46, 45])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl((m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))), (((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite(((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.47 tff(62,axiom,(![A: $i, B: $i] : ((l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_pre_topc')).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.47 tff(65,plain,(
% 0.20/0.47 ![A: $i, B: $i] : ((~(l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[64])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (~((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.47 inference(or_elim,[status(thm)],[68])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 ((m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (m1_subset_1(k6_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[75, 36, 69, 67])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl((v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A)) <=> (((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | v4_pre_topc(k6_pre_topc(A, B), A)))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | v4_pre_topc(k6_pre_topc(A, B), A)) <=> (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A)) <=> (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A)) <=> ![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v4_pre_topc(k6_pre_topc(A, B), A)) <=> ((v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v4_pre_topc(k6_pre_topc(A, B), A)))), rewrite(((v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v4_pre_topc(k6_pre_topc(A, B), A)) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))), ((((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v4_pre_topc(k6_pre_topc(A, B), A)) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (![A: $i, B: $i] : (((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v4_pre_topc(k6_pre_topc(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.48 tff(84,axiom,(![A: $i, B: $i] : (((v2_pre_topc(A) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => v4_pre_topc(k6_pre_topc(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_tops_1')).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.48 tff(87,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | v4_pre_topc(k6_pre_topc(A, B), A))),
% 0.20/0.48 inference(skolemize,[status(sab)],[86])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | v4_pre_topc(k6_pre_topc(A!0, C!2), A!0))) <=> ((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | v4_pre_topc(k6_pre_topc(A!0, C!2), A!0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 ((v4_pre_topc(k6_pre_topc(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | v4_pre_topc(k6_pre_topc(A!0, C!2), A!0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v4_pre_topc(k6_pre_topc(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v4_pre_topc(k6_pre_topc(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | v4_pre_topc(k6_pre_topc(A!0, C!2), A!0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v4_pre_topc(k6_pre_topc(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (v4_pre_topc(k6_pre_topc(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[95, 37, 36, 69, 89])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (~(k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2))))),
% 0.20/0.48 inference(or_elim,[status(thm)],[68])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))) | (~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))) | (~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (((~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2))))) <=> ((k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))) | (~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))) | (~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))) | (~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[100, 98])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | ((~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0)) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(C, A!0)) | (C = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, C))))) | (k6_pre_topc(A!0, C!2) = k3_tex_4(A!0, k5_subset_1(u1_struct_0(A!0), B!1, k6_pre_topc(A!0, C!2)))) | (~m1_subset_1(k6_pre_topc(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_pre_topc(k6_pre_topc(A!0, C!2), A!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[103, 97, 96, 76, 54])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------